Scholar’s Advanced Technological System

Looking at Lu Zhou slyly, staring at him for about half a minute, Morina suddenly reached out.

Looking towards the hand that touched his forehead, Lu Zhou subconsciously hid.

“What do you want to do?”

If he retracted his hand, Morina said in a serious way: “Nothing, I just want to see if you have a fever?”

Lu Zhou: “…”

Looking seriously at Lu Zhou, Morina continued: “Really, although I have not studied partial differential equations, why do you have to make the problem so complicated?”

Lu Zhou patted the grass on his trousers and stood up.

“I also want to make it simple, but there is no way, it is so complicated.”

Morina also stood up and walked up to Lu Zhou: “If a calculation has violated basic common sense, then it has a high probability of something going wrong.”

Lu Zhou did not deny her claim.

“Maybe you are correct, because I think so. However, compared to the solution of the three-dimensional NS equation, whether there is global regularity at a particular point, I would like to know, 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 authors in foreign literature like to use the word “Blow-up” to describe this troublesome phenomenon.

In mathematics, there are a lot of problems, for example, the process denominator of the solution may be 0, or the matrix of the solution may not converge…

For the NS equation, the so-called explosion problem, or divergence problem, refers to a certain point in time and a certain spatial point, the fluid flow rate is getting faster and faster, and the speed tends to infinity, which is beyond the common sense. .

Lionsand the 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 situation, there is still no unified conclusion in the academic world.

The general view of the mathematics community is optimistic about the existence and smoothness of the NS equation solution in the three-dimensional case. People who are engaged in the direction of computational fluid mechanics certainly agree with this because of the fart. The stock problem, otherwise, they are based on experimental data. Are those phenomenological models established that are not equivalent to using lies to explain lies?

Returning home with a sweat, Lu Zhou threw the clothes into the washing machine and turned to take a shower in the bathroom.

The feeling of hot water flowing down from the head made his impetuous calm a lot.

The idea of ​​indirect proofing through abstract double Linear operations may be problematic. Instead of entangled in uncertain problems, it is better to be prepared, such as trying another way.

This kind of game that challenges the human mind, Peak, has no solution to the problem itself.

Before the Karabi conjecture was resolved, the differential geometry community never imagined that partial differential equations and Riemannian geometry could still be played. After the Karabi conjecture was solved, the geometric analysis based on the PDE method came into being.

Not sure, while solving the NS equation, he can find more great things from it.

After returning to the study, he opened the computer and began to retrieve the literature on the NS equation.

After all is the century-old problem rewarded by the Cray Institute, the NS equation has a pivotal position in the field of partial differentials, so the Scholars of the partial differential equations have made many beautiful research results around this equation.

Whenever research falls into bottleneck, Lu Zhou tries to find the piece of puzzle that he lacks by searching thesis from the database.

Just as Perelman saw this method of Hamilton’s understanding of Ricci’s singularity, he immediately applied this method to solve the Poincaré conjecture, and he was looking for something similar.

however……

It is obviously not that simple to find this piece of puzzle.

The sunset outside the window has been covered with stars, and the hour hand of the wall clock has also passed the 12 point and began to shift towards the 1 point.

With a sigh of relief, Lu Zhou leaned back in the chair and pinched some sour eyebrows.

The erratic thoughts in his mind, like the almost solid ink, turned into a divergent smoke column for a while, which was a headache.

However, in this vagueness, Lu Zhou suddenly had a clear comprehension in his heart.

“If you don’t have tools, why don’t you make one yourself…”

If you abstract each molecule into a point and abstract the collection of these points into a space with local Euclidean spatial properties, he can construct an approximate three-dimensional manifold based on this, and the method of topology. Go in…

This seems to make the “simple” problem more “complex”.

But it seems…

Is it work?

The eyes are getting brighter and brighter.

Grabbing the inspiration in the darkness, Lu Zhou quickly grabbed the ballpoint pen and wrote a line on the paper.

[Lu manifold]

Then, the pen in his hand could not stop…

……

When you are fully immersed in a job, time always goes very fast.

In a blink of an eye, it is April.

During this one-and-a-half-year period, Lu Zhou, who was locked in the house, had a short and monotonous spring break.

During this time, in addition to Vera once came to his house and sent him a teaching report for this period of time, Lu Zhou almost cut off communication with the outside world.

In fact, although those things were brought to him by Vera, those things were sent to the corner of the study and almost never turned over.

At Princeton, Lu’s unique approach to research is almost an anecdote, and even undergraduates who have been enrolled in college have heard of it from old people.

Perhaps it was known that his research entered a critical period, and the Fefman Professor did not bother him, but temporarily stopped the regular exchange meeting and began separate research at the same time.

Now, these efforts have finally come to fruition.

Stopped the pen in his hand and looked at the stack of draft paper in front of him. Lu Zhou’s mouth smirked a smile.

Lu Zhou, whose taut string in the brain finally relaxed, began to think of something that was irrelevant.

For example, the name of the Lu manifold is not a bit too good to hear?

Do you want to change to LZ stream or LuZhu stream?

Thinking about it, Lu Zhou feels that it is better not to be a candidate for future generations.

The former seems to be prone to strange ambiguities, and the latter is not easy to read.

“The Chinese name is called Lu’s manifold, and the English translation is L-shaped, referred to as L-flow!”

Satisfied with the name, Lu Zhou changed the title on the manuscript paper, and then placed the papers on the corner of the table, ready to organize the contents into the computer one by one.

Just when he just turned on the computer and was about to start the work, a bunch of bubbles popped up in the work bar at the bottom right corner of the screen.

Xiao AI : [Master, have new mail! ()

Seeing this news, Lu Zhou tapped the link that Xiao AI threw and logged into the mailbox.

The email was sent in the annual issue of mathematics.

As for the content, it is naturally the thesis that proves the corner valley conjecture.

Seeing the end of the message from the beginning, Lu Zhou’s face once again showed a smile.

Although it was an unexpected thing, after seeing this email, he was sincerely happy for his students.

According to the decision of the editorial department of the annual edition of the mathematics, their thesis will be published in the latest issue of the journal and will be tested by the entire mathematics community…