After staring at Lu Zhou blankly for about half a minute, Molina suddenly stretched out her hand.
Eyes are getting brighter and brighter.
Looking at the hand touching his forehead, Lu Zhou subconsciously avoided it.
Just when he turned on the computer and was about to start this work, a series of bubbles suddenly popped up in the task bar in the lower right corner of the screen.
Just like Perelman immediately applied this method to solve the Poincaré conjecture after seeing Hamilton's paper on understanding Ricci flow singularities, he was also looking for something similar.
"Why our equations exploded."
Looking at the hand touching his forehead, Lu Zhou subconsciously avoided it.
"Maybe you are right, because I think so too. However, rather than whether the solution to the three-dimensional NS equation has global regularity at a particular point, what I want to know more is, why?"
After returning home covered in sweat, Lu Zhou threw his clothes into the washing machine and went to the bathroom to take a shower.
Before the Calabi conjecture was solved, the differential geometry community never thought that partial differential equations and Riemannian geometry could still play like this. After the Calabi conjecture was solved, geometric analysis based on the PDE method came into being.
Molina also stood up and walked to Lu Zhou: "If a calculation result violates basic common sense, then there is a high probability that there is something wrong with it."
…
And now, these efforts are finally bearing fruit.
Finding this piece of the puzzle is obviously not that simple.
"What do you want to do?"
Is it feasible
But it seems…
Catching a hint of inspiration, Lu Zhou quickly grabbed a ballpoint pen and wrote a line of words on the paper.
"Why our equations exploded."
This kind of game that challenges the peak of human mind has no formula for solving problems.
Withdrawing her hand as if nothing had happened, Molina said seriously: "It's nothing, I just want to see if you have a fever?"
In fact, although he asked Vera to send those things, he put them in the corner of the study after they were delivered, and rarely looked through them.
"Explosion" can also be called divergence in the field of computational fluid dynamics. Some authors in many foreign literature like to use the word "Blow-up" to describe this troublesome phenomenon.
Stopping the pen in his hand and looking at the pile of draft paper in front of him, Lu Zhou had a smile on his lips.
Lu Zhou: "..."
However…
Stopping the pen in his hand and looking at the pile of draft paper in front of him, Lu Zhou had a smile on his lips.
Then, the pen in his hand couldn't stop...
"Why our equations exploded."
The erratic thoughts in his mind were like almost solidified ink for one moment, and then turned into diverging smoke pillars for another, which made people feel headache.
…
Perhaps knowing that his research had entered a critical period, Professor Fefferman was considerate and did not disturb him. Instead, he temporarily stopped regular communication meetings and began to conduct independent research separately and simultaneously.
Looking at Lu Zhou seriously, Molina continued: "Seriously, although I have never studied partial differential equations, why do you want to make the problem so complicated?"
Looking at Lu Zhou seriously, Molina continued: "Seriously, although I have never studied partial differential equations, why do you want to make the problem so complicated?"
As for the content, it is naturally the paper on the proof of Kakutani’s conjecture.
Lu Zhou patted the grass on his pants and stood up.
After all, it is the problem of the century that is being rewarded by the Clay Institute. The NS equation plays a decisive role in the field of partial differential equations. Therefore, scholars in the field of partial differential equations have also made many beautiful research results around this equation.
[Lu manifold]
Whenever his research reaches a bottleneck, Lu Zhou will try to find the missing piece of the puzzle by retrieving papers from the database.
In mathematics, it generally refers to many problems. For example, the denominator of the solution process may be 0, or the matrix to be solved may not have converged...
…
"I also want to make it simpler, but there's no way, it's just so complicated."
Eyes are getting brighter and brighter.
Catching a hint of inspiration, Lu Zhou quickly grabbed a ballpoint pen and wrote a line of words on the paper.
"The Chinese name is Lu's manifold, and the English translation is L manifold, or L flow for short!"
According to the decision of the editorial board of Annals of Mathematics, their papers will be published in the latest issue of the journal and accepted by the entire mathematical community...
Molina also stood up and walked to Lu Zhou: "If a calculation result violates basic common sense, then there is a high probability that there is something wrong with it."
As for the content, it is naturally the paper on the proof of Kakutani’s conjecture.
The sunset outside the window has been covered with stars, and the hour hand of the clock on the wall has passed 12 o'clock and started to move towards 1 o'clock.
Perhaps knowing that his research had entered a critical period, Professor Fefferman was considerate and did not disturb him. Instead, he temporarily stopped regular communication meetings and began to conduct independent research separately and simultaneously.
There may be problems with the idea of indirect proof through abstract bilinear operators. Instead of repeatedly struggling with uncertain issues, it is better to be prepared, such as trying an additional idea in a different way.
"If you don't have tools, why not make one yourself..."
The email was from "Annals of Mathematics".
Lu Zhou did not deny her statement.
After all, it is the problem of the century that is being rewarded by the Clay Institute. The NS equation plays a decisive role in the field of partial differential equations. Therefore, scholars in the field of partial differential equations have also made many beautiful research results around this equation.
"The Chinese name is Lu's manifold, and the English translation is L manifold, or L flow for short!"
"I also want to make it simpler, but there's no way, it's just so complicated."
However…
After reading the email from beginning to end, a smile appeared on Lu Zhou's face again.
For more than a month, Lu Zhou locked himself in the house and spent a short and monotonous spring break.
The erratic thoughts in his mind were like almost solidified ink for one moment, and then turned into diverging smoke pillars for another, which made people feel headache.
"Maybe you are right, because I think so too. However, rather than whether the solution to the three-dimensional NS equation has global regularity at a particular point, what I want to know more is, why?"
But it seems…
Seeing this message, Lu Zhou casually clicked on the link Xiao Ai threw over and logged in to his email.
"The Chinese name is Lu's manifold, and the English translation is L manifold, or L flow for short!"
Before the Calabi conjecture was solved, the differential geometry community never thought that partial differential equations and Riemannian geometry could still play like this. After the Calabi conjecture was solved, geometric analysis based on the PDE method came into being.
Looking at the hand touching his forehead, Lu Zhou subconsciously avoided it.
Lu Zhou patted the grass on his pants and stood up.
Lu Zhou paused for a moment and stared at the lake before continuing.
The feeling of hot water flowing down from his head calmed down his impatience a lot.
Feeling much more satisfied with the name, Lu Zhou casually changed the title on the manuscript paper, then stacked the papers and placed them on the corner of the table, preparing to organize the contents onto the computer one by one.
"Why our equations exploded."
This kind of game that challenges the peak of human mind has no formula for solving problems.
In mathematics, it generally refers to many problems. For example, the denominator of the solution process may be 0, or the matrix to be solved may not have converged...
"If you don't have tools, why not make one yourself..."
The former seems prone to strange ambiguities, and the latter is not easy to read.
After taking a deep breath, Lu Zhou leaned on the chair and pinched his sore eyebrows.
…
If each molecule is abstracted into a point, and the set containing these points is abstracted into a space with local Euclidean space properties, he can completely construct an approximate three-dimensional manifold based on this, and use topological methods Go in…
According to the decision of the editorial board of Annals of Mathematics, their papers will be published in the latest issue of the journal and accepted by the entire mathematical community...
…
Lu Zhou paused for a moment and stared at the lake before continuing.
"Explosion" can also be called divergence in the field of computational fluid dynamics. Some authors in many foreign literature like to use the word "Blow-up" to describe this troublesome phenomenon.
Lu Zhou patted the grass on his pants and stood up.
Stopping the pen in his hand and looking at the pile of draft paper in front of him, Lu Zhou had a smile on his lips.
And now, these efforts are finally bearing fruit.
The former seems prone to strange ambiguities, and the latter is not easy to read.
…
Then, the pen in his hand couldn't stop...
In mathematics, it generally refers to many problems. For example, the denominator of the solution process may be 0, or the matrix to be solved may not have converged...
Time flies when you are immersed in a task.
Maybe, while solving the NS equation, he might discover something greater from it
The feeling of hot water flowing down from his head calmed down his impatience a lot.
Feeling much more satisfied with the name, Lu Zhou casually changed the title on the manuscript paper, then stacked the papers and placed them on the corner of the table, preparing to organize the contents onto the computer one by one.
Eyes are getting brighter and brighter.
For NS equations, the so-called explosion problem, or divergence problem, refers to a certain point in time and a certain point in space. The fluid flow rate is getting faster and faster, and then the speed tends to infinity, which is beyond common sense in reality. .
For more than a month, Lu Zhou locked himself in the house and spent a short and monotonous spring break.
How about changing it to LZ flow or LuZhu flow
Stopping the pen in his hand and looking at the pile of draft paper in front of him, Lu Zhou had a smile on his lips.
Lions and others proved as early as half a century ago that this point does not exist in the two-dimensional case, that is, the uniqueness, regularity and stability of the overall weak solution of the NS equation in the two-dimensional case. But what is the situation of the NS equation in the three-dimensional case? There is still no unified conclusion in the academic community.
After returning home covered in sweat, Lu Zhou threw his clothes into the washing machine and went to the bathroom to take a shower.
Molina also stood up and walked to Lu Zhou: "If a calculation result violates basic common sense, then there is a high probability that there is something wrong with it."
After staring at Lu Zhou blankly for about half a minute, Molina suddenly stretched out her hand.
Just when he turned on the computer and was about to start this work, a series of bubbles suddenly popped up in the task bar in the lower right corner of the screen.
The general view in the mathematical community is optimistic about the existence and smoothness of solutions to NS equations in three dimensions. People in the field of computational fluid dynamics certainly agree with this because of the butt problem - otherwise, those they established based on experimental data Isn’t the phenomenological model tantamount to using lies to explain lies
"What do you want to do?"
Stopping the pen in his hand and looking at the pile of draft paper in front of him, Lu Zhou had a smile on his lips.
Xiao Ai: [Master, there is a new email!]
Stopping the pen in his hand and looking at the pile of draft paper in front of him, Lu Zhou had a smile on his lips.
The tense string in his mind finally relaxed, and Lu Zhou began to think of some insignificant things.
"What do you want to do?"
…
Maybe, while solving the NS equation, he might discover something greater from it
After returning home covered in sweat, Lu Zhou threw his clothes into the washing machine and went to the bathroom to take a shower.
The erratic thoughts in his mind were like almost solidified ink for one moment, and then turned into diverging smoke pillars for another, which made people feel headache.
As for the content, it is naturally the paper on the proof of Kakutani’s conjecture.
The feeling of hot water flowing down from his head calmed down his impatience a lot.
During this period of time, except for Vera who came to his house once and gave him a teaching report during this period, Lu Zhou almost cut off communication with the outside world.
After thinking about it, Lu Zhou felt that it would be better not to embarrass future generations of candidates.
…
For NS equations, the so-called explosion problem, or divergence problem, refers to a certain point in time and a certain point in space. The fluid flow rate is getting faster and faster, and then the speed tends to infinity, which is beyond common sense in reality. .
How about changing it to LZ flow or LuZhu flow
In fact, although he asked Vera to send those things, he put them in the corner of the study after they were delivered, and rarely looked through them.
Perhaps knowing that his research had entered a critical period, Professor Fefferman was considerate and did not disturb him. Instead, he temporarily stopped regular communication meetings and began to conduct independent research separately and simultaneously.
There may be problems with the idea of indirect proof through abstract bilinear operators. Instead of repeatedly struggling with uncertain issues, it is better to be prepared, such as trying an additional idea in a different way.
After returning home covered in sweat, Lu Zhou threw his clothes into the washing machine and went to the bathroom to take a shower.
If each molecule is abstracted into a point, and the set containing these points is abstracted into a space with local Euclidean space properties, he can completely construct an approximate three-dimensional manifold based on this, and use topological methods Go in…
Maybe, while solving the NS equation, he might discover something greater from it
However…
Time flies when you are immersed in a task.
There may be problems with the idea of indirect proof through abstract bilinear operators. Instead of repeatedly struggling with uncertain issues, it is better to be prepared, such as trying an additional idea in a different way.
This kind of game that challenges the peak of human mind has no formula for solving problems.
Looking at Lu Zhou seriously, Molina continued: "Seriously, although I have never studied partial differential equations, why do you want to make the problem so complicated?"
Just when he turned on the computer and was about to start this work, a series of bubbles suddenly popped up in the task bar in the lower right corner of the screen.
The erratic thoughts in his mind were like almost solidified ink for one moment, and then turned into diverging smoke pillars for another, which made people feel headache.
Looking at Lu Zhou seriously, Molina continued: "Seriously, although I have never studied partial differential equations, why do you want to make the problem so complicated?"
"Maybe you are right, because I think so too. However, rather than whether the solution to the three-dimensional NS equation has global regularity at a particular point, what I want to know more is, why?"
And now, these efforts are finally bearing fruit.
Before the Calabi conjecture was solved, the differential geometry community never thought that partial differential equations and Riemannian geometry could still play like this. After the Calabi conjecture was solved, geometric analysis based on the PDE method came into being.
If each molecule is abstracted into a point, and the set containing these points is abstracted into a space with local Euclidean space properties, he can completely construct an approximate three-dimensional manifold based on this, and use topological methods Go in…
The email was from "Annals of Mathematics".
Maybe, while solving the NS equation, he might discover something greater from it
How about changing it to LZ flow or LuZhu flow
After reading the email from beginning to end, a smile appeared on Lu Zhou's face again.
"Maybe you are right, because I think so too. However, rather than whether the solution to the three-dimensional NS equation has global regularity at a particular point, what I want to know more is, why?"
Just when he turned on the computer and was about to start this work, a series of bubbles suddenly popped up in the task bar in the lower right corner of the screen.
Lu Zhou: "..."
Lions and others proved as early as half a century ago that this point does not exist in the two-dimensional case, that is, the uniqueness, regularity and stability of the overall weak solution of the NS equation in the two-dimensional case. But what is the situation of the NS equation in the three-dimensional case? There is still no unified conclusion in the academic community.
"Explosion" can also be called divergence in the field of computational fluid dynamics. Some authors in many foreign literature like to use the word "Blow-up" to describe this troublesome phenomenon.
After returning to the study, he turned on the computer and began to search for literature on NS equations.
The former seems prone to strange ambiguities, and the latter is not easy to read.
The sunset outside the window has been covered with stars, and the hour hand of the clock on the wall has passed 12 o'clock and started to move towards 1 o'clock.
If each molecule is abstracted into a point, and the set containing these points is abstracted into a space with local Euclidean space properties, he can completely construct an approximate three-dimensional manifold based on this, and use topological methods Go in…
The feeling of hot water flowing down from his head calmed down his impatience a lot.
The tense string in his mind finally relaxed, and Lu Zhou began to think of some insignificant things.
In mathematics, it generally refers to many problems. For example, the denominator of the solution process may be 0, or the matrix to be solved may not have converged...
After all, it is the problem of the century that is being rewarded by the Clay Institute. The NS equation plays a decisive role in the field of partial differential equations. Therefore, scholars in the field of partial differential equations have also made many beautiful research results around this equation.
The email was from "Annals of Mathematics".
After returning to the study, he turned on the computer and began to search for literature on NS equations.
After returning to the study, he turned on the computer and began to search for literature on NS equations.
Whenever his research reaches a bottleneck, Lu Zhou will try to find the missing piece of the puzzle by retrieving papers from the database.
For more than a month, Lu Zhou locked himself in the house and spent a short and monotonous spring break.
At Princeton, Professor Lu's unique way of delving into problems is almost an anecdote. Even undergraduates who have just enrolled have heard about it from old students.
Molina also stood up and walked to Lu Zhou: "If a calculation result violates basic common sense, then there is a high probability that there is something wrong with it."
And now, these efforts are finally bearing fruit.
For example, does the name Lu manifold sound a bit unpleasant
Stopping the pen in his hand and looking at the pile of draft paper in front of him, Lu Zhou had a smile on his lips.
Perhaps knowing that his research had entered a critical period, Professor Fefferman was considerate and did not disturb him. Instead, he temporarily stopped regular communication meetings and began to conduct independent research separately and simultaneously.
How about changing it to LZ flow or LuZhu flow
Just like Perelman immediately applied this method to solve the Poincaré conjecture after seeing Hamilton's paper on understanding Ricci flow singularities, he was also looking for something similar.
Lu Zhou patted the grass on his pants and stood up.
Time flies when you are immersed in a task.
How about changing it to LZ flow or LuZhu flow
Finding this piece of the puzzle is obviously not that simple.
However…
During this period of time, except for Vera who came to his house once and gave him a teaching report during this period, Lu Zhou almost cut off communication with the outside world.
Lu Zhou patted the grass on his pants and stood up.
Lu Zhou did not deny her statement.
Lu Zhou patted the grass on his pants and stood up.
Molina also stood up and walked to Lu Zhou: "If a calculation result violates basic common sense, then there is a high probability that there is something wrong with it."
Finding this piece of the puzzle is obviously not that simple.
The feeling of hot water flowing down from his head calmed down his impatience a lot.
Is it feasible
Then, the pen in his hand couldn't stop...
"If you don't have tools, why not make one yourself..."
The tense string in his mind finally relaxed, and Lu Zhou began to think of some insignificant things.
"Explosion" can also be called divergence in the field of computational fluid dynamics. Some authors in many foreign literature like to use the word "Blow-up" to describe this troublesome phenomenon.
However, in this vagueness, Lu Zhou suddenly felt a hint of enlightenment in his heart.
If each molecule is abstracted into a point, and the set containing these points is abstracted into a space with local Euclidean space properties, he can completely construct an approximate three-dimensional manifold based on this, and use topological methods Go in…
The sunset outside the window has been covered with stars, and the hour hand of the clock on the wall has passed 12 o'clock and started to move towards 1 o'clock.
As for the content, it is naturally the paper on the proof of Kakutani’s conjecture.
…
Stopping the pen in his hand and looking at the pile of draft paper in front of him, Lu Zhou had a smile on his lips.
The tense string in his mind finally relaxed, and Lu Zhou began to think of some insignificant things.
"Maybe you are right, because I think so too. However, rather than whether the solution to the three-dimensional NS equation has global regularity at a particular point, what I want to know more is, why?"
How about changing it to LZ flow or LuZhu flow
Lions and others proved as early as half a century ago that this point does not exist in the two-dimensional case, that is, the uniqueness, regularity and stability of the overall weak solution of the NS equation in the two-dimensional case. But what is the situation of the NS equation in the three-dimensional case? There is still no unified conclusion in the academic community.
At Princeton, Professor Lu's unique way of delving into problems is almost an anecdote. Even undergraduates who have just enrolled have heard about it from old students.
After taking a deep breath, Lu Zhou leaned on the chair and pinched his sore eyebrows.
Molina also stood up and walked to Lu Zhou: "If a calculation result violates basic common sense, then there is a high probability that there is something wrong with it."
After reading the email from beginning to end, a smile appeared on Lu Zhou's face again.
For example, does the name Lu manifold sound a bit unpleasant
The sunset outside the window has been covered with stars, and the hour hand of the clock on the wall has passed 12 o'clock and started to move towards 1 o'clock.
Looking at the hand touching his forehead, Lu Zhou subconsciously avoided it.
…
However, in this vagueness, Lu Zhou suddenly felt a hint of enlightenment in his heart.
The erratic thoughts in his mind were like almost solidified ink for one moment, and then turned into diverging smoke pillars for another, which made people feel headache.
For more than a month, Lu Zhou locked himself in the house and spent a short and monotonous spring break.
At Princeton, Professor Lu's unique way of delving into problems is almost an anecdote. Even undergraduates who have just enrolled have heard about it from old students.
Just when he turned on the computer and was about to start this work, a series of bubbles suddenly popped up in the task bar in the lower right corner of the screen.
At Princeton, Professor Lu's unique way of delving into problems is almost an anecdote. Even undergraduates who have just enrolled have heard about it from old students.
"Maybe you are right, because I think so too. However, rather than whether the solution to the three-dimensional NS equation has global regularity at a particular point, what I want to know more is, why?"
Perhaps knowing that his research had entered a critical period, Professor Fefferman was considerate and did not disturb him. Instead, he temporarily stopped regular communication meetings and began to conduct independent research separately and simultaneously.
Stopping the pen in his hand and looking at the pile of draft paper in front of him, Lu Zhou had a smile on his lips.
However, in this vagueness, Lu Zhou suddenly felt a hint of enlightenment in his heart.
For example, does the name Lu manifold sound a bit unpleasant
In fact, although he asked Vera to send those things, he put them in the corner of the study after they were delivered, and rarely looked through them.
"If you don't have tools, why not make one yourself..."
Lu Zhou did not deny her statement.
As for the content, it is naturally the paper on the proof of Kakutani’s conjecture.
If each molecule is abstracted into a point, and the set containing these points is abstracted into a space with local Euclidean space properties, he can completely construct an approximate three-dimensional manifold based on this, and use topological methods Go in…
Just like Perelman immediately applied this method to solve the Poincaré conjecture after seeing Hamilton's paper on understanding Ricci flow singularities, he was also looking for something similar.
According to the decision of the editorial board of Annals of Mathematics, their papers will be published in the latest issue of the journal and accepted by the entire mathematical community...
Seeing this message, Lu Zhou casually clicked on the link Xiao Ai threw over and logged in to his email.
Lu Zhou did not deny her statement.
This seems to make a "simple" problem more "complex".
"The Chinese name is Lu's manifold, and the English translation is L manifold, or L flow for short!"
Lu Zhou did not deny her statement.
Seeing this message, Lu Zhou casually clicked on the link Xiao Ai threw over and logged in to his email.
Molina also stood up and walked to Lu Zhou: "If a calculation result violates basic common sense, then there is a high probability that there is something wrong with it."
The sunset outside the window has been covered with stars, and the hour hand of the clock on the wall has passed 12 o'clock and started to move towards 1 o'clock.
Feeling much more satisfied with the name, Lu Zhou casually changed the title on the manuscript paper, then stacked the papers and placed them on the corner of the table, preparing to organize the contents onto the computer one by one.
As for the content, it is naturally the paper on the proof of Kakutani’s conjecture.
But it seems…
At Princeton, Professor Lu's unique way of delving into problems is almost an anecdote. Even undergraduates who have just enrolled have heard about it from old students.
Just when he turned on the computer and was about to start this work, a series of bubbles suddenly popped up in the task bar in the lower right corner of the screen.
In fact, although he asked Vera to send those things, he put them in the corner of the study after they were delivered, and rarely looked through them.
After all, it is the problem of the century that is being rewarded by the Clay Institute. The NS equation plays a decisive role in the field of partial differential equations. Therefore, scholars in the field of partial differential equations have also made many beautiful research results around this equation.
Before the Calabi conjecture was solved, the differential geometry community never thought that partial differential equations and Riemannian geometry could still play like this. After the Calabi conjecture was solved, geometric analysis based on the PDE method came into being.
Catching a hint of inspiration, Lu Zhou quickly grabbed a ballpoint pen and wrote a line of words on the paper.
If each molecule is abstracted into a point, and the set containing these points is abstracted into a space with local Euclidean space properties, he can completely construct an approximate three-dimensional manifold based on this, and use topological methods Go in…
Is it feasible
If each molecule is abstracted into a point, and the set containing these points is abstracted into a space with local Euclidean space properties, he can completely construct an approximate three-dimensional manifold based on this, and use topological methods Go in…
Molina also stood up and walked to Lu Zhou: "If a calculation result violates basic common sense, then there is a high probability that there is something wrong with it."
Eyes are getting brighter and brighter.
However, in this vagueness, Lu Zhou suddenly felt a hint of enlightenment in his heart.
Feeling much more satisfied with the name, Lu Zhou casually changed the title on the manuscript paper, then stacked the papers and placed them on the corner of the table, preparing to organize the contents onto the computer one by one.
The feeling of hot water flowing down from his head calmed down his impatience a lot.
Catching a hint of inspiration, Lu Zhou quickly grabbed a ballpoint pen and wrote a line of words on the paper.
In mathematics, it generally refers to many problems. For example, the denominator of the solution process may be 0, or the matrix to be solved may not have converged...
Lu Zhou did not deny her statement.
"If you don't have tools, why not make one yourself..."
Before the Calabi conjecture was solved, the differential geometry community never thought that partial differential equations and Riemannian geometry could still play like this. After the Calabi conjecture was solved, geometric analysis based on the PDE method came into being.
Perhaps knowing that his research had entered a critical period, Professor Fefferman was considerate and did not disturb him. Instead, he temporarily stopped regular communication meetings and began to conduct independent research separately and simultaneously.
This kind of game that challenges the peak of human mind has no formula for solving problems.
[Lu manifold]
After all, it is the problem of the century that is being rewarded by the Clay Institute. The NS equation plays a decisive role in the field of partial differential equations. Therefore, scholars in the field of partial differential equations have also made many beautiful research results around this equation.
In mathematics, it generally refers to many problems. For example, the denominator of the solution process may be 0, or the matrix to be solved may not have converged...
Looking at the hand touching his forehead, Lu Zhou subconsciously avoided it.
Then, the pen in his hand couldn't stop...
For more than a month, Lu Zhou locked himself in the house and spent a short and monotonous spring break.
Just like Perelman immediately applied this method to solve the Poincaré conjecture after seeing Hamilton's paper on understanding Ricci flow singularities, he was also looking for something similar.
…
In a blink of an eye, it’s April.
"If you don't have tools, why not make one yourself..."
Before the Calabi conjecture was solved, the differential geometry community never thought that partial differential equations and Riemannian geometry could still play like this. After the Calabi conjecture was solved, geometric analysis based on the PDE method came into being.
Time flies when you are immersed in a task.
After returning to the study, he turned on the computer and began to search for literature on NS equations.
Just when he turned on the computer and was about to start this work, a series of bubbles suddenly popped up in the task bar in the lower right corner of the screen.
Time flies when you are immersed in a task.
Whenever his research reaches a bottleneck, Lu Zhou will try to find the missing piece of the puzzle by retrieving papers from the database.
Lu Zhou did not deny her statement.
For NS equations, the so-called explosion problem, or divergence problem, refers to a certain point in time and a certain point in space. The fluid flow rate is getting faster and faster, and then the speed tends to infinity, which is beyond common sense in reality. .
In mathematics, it generally refers to many problems. For example, the denominator of the solution process may be 0, or the matrix to be solved may not have converged...
Is it feasible
In a blink of an eye, it’s April.
After all, it is the problem of the century that is being rewarded by the Clay Institute. The NS equation plays a decisive role in the field of partial differential equations. Therefore, scholars in the field of partial differential equations have also made many beautiful research results around this equation.
Time flies when you are immersed in a task.
For more than a month, Lu Zhou locked himself in the house and spent a short and monotonous spring break.
However, in this vagueness, Lu Zhou suddenly felt a hint of enlightenment in his heart.
In mathematics, it generally refers to many problems. For example, the denominator of the solution process may be 0, or the matrix to be solved may not have converged...
During this period of time, except for Vera who came to his house once and gave him a teaching report during this period, Lu Zhou almost cut off communication with the outside world.
Lu Zhou did not deny her statement.
Whenever his research reaches a bottleneck, Lu Zhou will try to find the missing piece of the puzzle by retrieving papers from the database.
After taking a deep breath, Lu Zhou leaned on the chair and pinched his sore eyebrows.
Catching a hint of inspiration, Lu Zhou quickly grabbed a ballpoint pen and wrote a line of words on the paper.
Lu Zhou: "..."
In fact, although he asked Vera to send those things, he put them in the corner of the study after they were delivered, and rarely looked through them.
If each molecule is abstracted into a point, and the set containing these points is abstracted into a space with local Euclidean space properties, he can completely construct an approximate three-dimensional manifold based on this, and use topological methods Go in…
How about changing it to LZ flow or LuZhu flow
"Maybe you are right, because I think so too. However, rather than whether the solution to the three-dimensional NS equation has global regularity at a particular point, what I want to know more is, why?"
Finding this piece of the puzzle is obviously not that simple.
The sunset outside the window has been covered with stars, and the hour hand of the clock on the wall has passed 12 o'clock and started to move towards 1 o'clock.
Just like Perelman immediately applied this method to solve the Poincaré conjecture after seeing Hamilton's paper on understanding Ricci flow singularities, he was also looking for something similar.
…
However, in this vagueness, Lu Zhou suddenly felt a hint of enlightenment in his heart.
At Princeton, Professor Lu's unique way of delving into problems is almost an anecdote. Even undergraduates who have just enrolled have heard about it from old students.
This seems to make a "simple" problem more "complex".
However…
Perhaps knowing that his research had entered a critical period, Professor Fefferman was considerate and did not disturb him. Instead, he temporarily stopped regular communication meetings and began to conduct independent research separately and simultaneously.
Withdrawing her hand as if nothing had happened, Molina said seriously: "It's nothing, I just want to see if you have a fever?"
Just when he turned on the computer and was about to start this work, a series of bubbles suddenly popped up in the task bar in the lower right corner of the screen.
But it seems…
Feeling much more satisfied with the name, Lu Zhou casually changed the title on the manuscript paper, then stacked the papers and placed them on the corner of the table, preparing to organize the contents onto the computer one by one.
And now, these efforts are finally bearing fruit.
After staring at Lu Zhou blankly for about half a minute, Molina suddenly stretched out her hand.
And now, these efforts are finally bearing fruit.
This kind of game that challenges the peak of human mind has no formula for solving problems.
As for the content, it is naturally the paper on the proof of Kakutani’s conjecture.
Time flies when you are immersed in a task.
…
The tense string in his mind finally relaxed, and Lu Zhou began to think of some insignificant things.
Stopping the pen in his hand and looking at the pile of draft paper in front of him, Lu Zhou had a smile on his lips.
Lu Zhou patted the grass on his pants and stood up.
Seeing this message, Lu Zhou casually clicked on the link Xiao Ai threw over and logged in to his email.
The tense string in his mind finally relaxed, and Lu Zhou began to think of some insignificant things.
According to the decision of the editorial board of Annals of Mathematics, their papers will be published in the latest issue of the journal and accepted by the entire mathematical community...
After reading the email from beginning to end, a smile appeared on Lu Zhou's face again.
After staring at Lu Zhou blankly for about half a minute, Molina suddenly stretched out her hand.
The tense string in his mind finally relaxed, and Lu Zhou began to think of some insignificant things.
Time flies when you are immersed in a task.
Lu Zhou did not deny her statement.
"I also want to make it simpler, but there's no way, it's just so complicated."
In a blink of an eye, it’s April.
In mathematics, it generally refers to many problems. For example, the denominator of the solution process may be 0, or the matrix to be solved may not have converged...
Withdrawing her hand as if nothing had happened, Molina said seriously: "It's nothing, I just want to see if you have a fever?"
For example, does the name Lu manifold sound a bit unpleasant
However…
Molina also stood up and walked to Lu Zhou: "If a calculation result violates basic common sense, then there is a high probability that there is something wrong with it."
Just when he turned on the computer and was about to start this work, a series of bubbles suddenly popped up in the task bar in the lower right corner of the screen.
How about changing it to LZ flow or LuZhu flow
Withdrawing her hand as if nothing had happened, Molina said seriously: "It's nothing, I just want to see if you have a fever?"
"If you don't have tools, why not make one yourself..."
Just when he turned on the computer and was about to start this work, a series of bubbles suddenly popped up in the task bar in the lower right corner of the screen.
The general view in the mathematical community is optimistic about the existence and smoothness of solutions to NS equations in three dimensions. People in the field of computational fluid dynamics certainly agree with this because of the butt problem - otherwise, those they established based on experimental data Isn’t the phenomenological model tantamount to using lies to explain lies
"The Chinese name is Lu's manifold, and the English translation is L manifold, or L flow for short!"
After thinking about it, Lu Zhou felt that it would be better not to embarrass future generations of candidates.
"What do you want to do?"
After thinking about it, Lu Zhou felt that it would be better not to embarrass future generations of candidates.
And now, these efforts are finally bearing fruit.
After staring at Lu Zhou blankly for about half a minute, Molina suddenly stretched out her hand.
According to the decision of the editorial board of Annals of Mathematics, their papers will be published in the latest issue of the journal and accepted by the entire mathematical community...
There may be problems with the idea of indirect proof through abstract bilinear operators. Instead of repeatedly struggling with uncertain issues, it is better to be prepared, such as trying an additional idea in a different way.
The email was from "Annals of Mathematics".
"What do you want to do?"
Stopping the pen in his hand and looking at the pile of draft paper in front of him, Lu Zhou had a smile on his lips.
The former seems prone to strange ambiguities, and the latter is not easy to read.
The general view in the mathematical community is optimistic about the existence and smoothness of solutions to NS equations in three dimensions. People in the field of computational fluid dynamics certainly agree with this because of the butt problem - otherwise, those they established based on experimental data Isn’t the phenomenological model tantamount to using lies to explain lies
However…
The email was from "Annals of Mathematics".
"The Chinese name is Lu's manifold, and the English translation is L manifold, or L flow for short!"
"Explosion" can also be called divergence in the field of computational fluid dynamics. Some authors in many foreign literature like to use the word "Blow-up" to describe this troublesome phenomenon.
After reading the email from beginning to end, a smile appeared on Lu Zhou's face again.
But it seems…
Xiao Ai: [Master, there is a new email!]
Feeling much more satisfied with the name, Lu Zhou casually changed the title on the manuscript paper, then stacked the papers and placed them on the corner of the table, preparing to organize the contents onto the computer one by one.
After returning home covered in sweat, Lu Zhou threw his clothes into the washing machine and went to the bathroom to take a shower.
Looking at Lu Zhou seriously, Molina continued: "Seriously, although I have never studied partial differential equations, why do you want to make the problem so complicated?"
After returning to the study, he turned on the computer and began to search for literature on NS equations.
After taking a deep breath, Lu Zhou leaned on the chair and pinched his sore eyebrows.
In mathematics, it generally refers to many problems. For example, the denominator of the solution process may be 0, or the matrix to be solved may not have converged...
Just when he turned on the computer and was about to start this work, a series of bubbles suddenly popped up in the task bar in the lower right corner of the screen.
After thinking about it, Lu Zhou felt that it would be better not to embarrass future generations of candidates.
The email was from "Annals of Mathematics".
After staring at Lu Zhou blankly for about half a minute, Molina suddenly stretched out her hand.
After thinking about it, Lu Zhou felt that it would be better not to embarrass future generations of candidates.
And now, these efforts are finally bearing fruit.
…
Perhaps knowing that his research had entered a critical period, Professor Fefferman was considerate and did not disturb him. Instead, he temporarily stopped regular communication meetings and began to conduct independent research separately and simultaneously.
Xiao Ai: [Master, there is a new email!]
[Lu manifold]
Before the Calabi conjecture was solved, the differential geometry community never thought that partial differential equations and Riemannian geometry could still play like this. After the Calabi conjecture was solved, geometric analysis based on the PDE method came into being.
Xiao Ai: [Master, there is a new email!]
Before the Calabi conjecture was solved, the differential geometry community never thought that partial differential equations and Riemannian geometry could still play like this. After the Calabi conjecture was solved, geometric analysis based on the PDE method came into being.
Lu Zhou did not deny her statement.
Seeing this message, Lu Zhou casually clicked on the link Xiao Ai threw over and logged in to his email.
"What do you want to do?"
Looking at the hand touching his forehead, Lu Zhou subconsciously avoided it.
Time flies when you are immersed in a task.
Just like Perelman immediately applied this method to solve the Poincaré conjecture after seeing Hamilton's paper on understanding Ricci flow singularities, he was also looking for something similar.
The email was from "Annals of Mathematics".
Feeling much more satisfied with the name, Lu Zhou casually changed the title on the manuscript paper, then stacked the papers and placed them on the corner of the table, preparing to organize the contents onto the computer one by one.
Time flies when you are immersed in a task.
If each molecule is abstracted into a point, and the set containing these points is abstracted into a space with local Euclidean space properties, he can completely construct an approximate three-dimensional manifold based on this, and use topological methods Go in…
The erratic thoughts in his mind were like almost solidified ink for one moment, and then turned into diverging smoke pillars for another, which made people feel headache.
As for the content, it is naturally the paper on the proof of Kakutani’s conjecture.
…
Catching a hint of inspiration, Lu Zhou quickly grabbed a ballpoint pen and wrote a line of words on the paper.
After reading the email from beginning to end, a smile appeared on Lu Zhou's face again.
After taking a deep breath, Lu Zhou leaned on the chair and pinched his sore eyebrows.
Finding this piece of the puzzle is obviously not that simple.
Although it was expected, after seeing this email, he was sincerely happy for his students.
According to the decision of the editorial board of Annals of Mathematics, their papers will be published in the latest issue of the journal and accepted by the entire mathematical community...
After taking a deep breath, Lu Zhou leaned on the chair and pinched his sore eyebrows.
After returning to the study, he turned on the computer and began to search for literature on NS equations.
"Maybe you are right, because I think so too. However, rather than whether the solution to the three-dimensional NS equation has global regularity at a particular point, what I want to know more is, why?"
"I also want to make it simpler, but there's no way, it's just so complicated."
According to the decision of the editorial board of Annals of Mathematics, their papers will be published in the latest issue of the journal and accepted by the entire mathematical community...
After thinking about it, Lu Zhou felt that it would be better not to embarrass future generations of candidates.
Maybe, while solving the NS equation, he might discover something greater from it
However…
Lions and others proved as early as half a century ago that this point does not exist in the two-dimensional case, that is, the uniqueness, regularity and stability of the overall weak solution of the NS equation in the two-dimensional case. But what is the situation of the NS equation in the three-dimensional case? There is still no unified conclusion in the academic community.
As for the content, it is naturally the paper on the proof of Kakutani’s conjecture.