Chapter 412: Lu's manifold?

Looking at Lu Zhou dumbfounded, staring at him for about half a minute, Molina suddenly held out her hand.
Looking at the hand that touched his forehead, Lu Zhou avoided it subconsciously.
"What do you want to do?"
If she withdrew her hand casually, Molina said solemnly: "Nothing, I just want to see if you have a fever?"
Lu Zhou: "..."
Looking at Lu Zhou seriously, Molina continued: "Seriously, although I haven't studied partial differential equations, why did you make the problem so complicated?"
Lu Zhou patted the grass on his pants and stood up.
"I also want to make it simple, but there is no way it is so complicated."
Molina also stood up and walked in front of Lu Zhou: "If a calculation result has violated basic common sense, then there is a high probability that something went wrong."
Lu Zhou did not deny her claims.
"Maybe you are right, because I think so. But compared to the three-dimensional NS equation, the solution has global regularity at a particular point. What I want to know is why?"
After a pause, Lu Zhou staring at the lake continued.
"Why our equation exploded."
...
"Explosion" can also be called divergence in the field of computational fluid dynamics. Some foreign authors like to use the term "Blow-up" to describe this headache.
In mathematics, it also refers to many problems, for example, the denominator of the solution process may be 0, and the solution matrix may not converge ...
For the NS equation, the so-called explosion problem, or divergence problem, refers to a certain time point and a certain space point, the fluid velocity is getting faster and faster, and the speed tends to infinity, which is beyond the common sense in reality. .
Et al. Proved 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 situation, the academic world still does not have a unified conclusion.
The general opinion in the mathematics community is optimistic about the existence and smoothness of the solution of the NS equation in three dimensions. Those who are engaged in computational fluid dynamics because of the fart. Of course, they agree with this. Otherwise, they build it based on experimental data Are those phenomenological models equivalent to using lies to explain lies?
Returning home with a sweat, Lu Zhou threw his clothes into the washing machine and turned to the bathroom to take a shower.
The feeling of hot water flowing from his head calmed his impetuousness.
The idea of ​​indirect proof through abstract bilinear operators may be problematic. Instead of repeatedly entanglement on uncertain issues, it is better to do two-handed preparation, such as trying another way of thinking.
This game, which challenges the peak of human mind, has no formula for solving problems.
Before the Calabi conjecture was solved, the world of differential geometry never expected that partial differential equations and Riemann geometry could be played like this. After the Calabi conjecture was solved, geometric analysis based on the PDE method came into being.
Maybe, while solving the NS equation, it is not necessarily that he can find something greater from it?
After returning to the study, he turned on the computer and began searching for literature on the NS equation.
After all, it is a century-old problem rewarded by the Clay Institute. The NS equation has a pivotal position in the field of partial differentials. Therefore, scholars in the field of partial differential equations have also made many beautiful research results around this equation.
Whenever research is bottlenecked, Lu Zhou will try to find the piece of puzzle he lacks by retrieving the paper from the database.
Just as Perelman applied this method to solving Poincaré's conjecture immediately after seeing Hamilton's dissertation on understanding Rii flow singularities, he was looking for something similar.
however……
Obviously, finding this piece of puzzle is not so simple.
The evening glow outside the window has been covered with stars, and the clock on the wall clock has passed 12 o'clock and started to shift towards 1 o'clock.
With a sigh of relief, Lu Zhou leaned back in his chair and squeezed some sour brows.
The erratic thoughts in his mind seemed like almost solid ink for a while, and then turned into a plume of smoke, which caused a headache.
However, also in this faintness, Lu Zhou's heart suddenly appeared a little enlightenment.
"Without tools, why not make one yourself ..."
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 construct an approximate three-dimensional manifold based on this, and use the topology method Go in ...
This seems to make the "simple" problem more "complex".
But it seems ...
Does it work?
Eyes are getting brighter.
Grasp a hint of inspiration, Lu Zhou quickly grabbed the ball-point pen and wrote a line on the paper.
[Lu manifold]
Then, the pen in his hand couldn't stop ...
...
When immersed in a job, time always passes quickly.
In a flash, it was April.
During this more than a month, I landed myself in a house on a land boat, and also spent a short and monotonous spring break.
During this time, in addition to Willa coming to his house once and sending him a teaching report during this time, Lu Zhou almost cut off communication with the outside world.
In fact, although he sent Vera to those things, he put them in the corner of the study after he delivered them, and almost never turned them over.
In Princeton, Professor Lu's unique way of delving into problems can almost be regarded as an anecdote. Even undergraduates who have just enrolled have heard from old students.
Perhaps knowing that his research has entered a critical period, Professor Fefferman also thoughtfully did not disturb him, but temporarily stopped regular communication meetings and started independent research at the same time.
Now, these efforts have finally come to fruition.
He stopped the pen in his hand and looked at the stack of draft paper in front of him.
The tense string in his head finally relaxed, and Lu Zhou began to think of something insignificant.
For example, is the name Lu Manifold a bit unpleasant?
Should it be changed to LZ stream or LuZhu stream?
After thinking about it, Lu Zhou felt that it was better not to embarrass the candidates in future generations.
The former seems to be prone to strange ambiguities, while the latter is not easy to read.
"The Chinese name is called the Lu Manifold. The English translation is L Manifold, which is referred to as L Manifold!"
I am more satisfied with this name ~ EbookFREE.me ~ Lu Zhou changed the title of the manuscript paper at will, and then put these papers in the corner of the table, ready to organize them on the computer one by one.
Just when he turned on the computer and was about to start the job, a string of bubbles popped up in the task bar in the lower right corner of the screen.
Xiao Ai: [Master, there is a new mail! (??????) ??】
Seeing this news, Lu Zhou clicked on the link thrown by Xiao Ai and logged in to his mailbox.
The e-mail is from the "Mathematics Yearbook".
As for the content, it is naturally the paper on Kakutani's conjecture.
After seeing the mail from the beginning to the end, a smile appeared on Lu Zhou's face again.
Although it was expected, after seeing this email, he was sincerely happy for his students.
According to the decision of the editorial department of the "Mathematics Annual", their paper will be published in the latest issue of the journal, and will be tested by the entire mathematical community ...