Looking at Lu Zhou in a daze, staring at him for about half a minute, Mo Lina suddenly stretched out her hand.

Looking at the hand that touched his forehead, Lu Zhou subconsciously dodged.

"What do you want to do?"

Withdrawing her hand casually, Molina said solemnly: "It's nothing, I just want to see, do you have a fever?" ”

Lu Zhou: "......"

Looking at Lu Zhou seriously, Molina continued: "Seriously, although I haven't studied partial differential equations, why do you make the problem so complicated? ”

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

"I wanted to make it simpler, but I can't help it, it's just that complicated."

Mo Lina also stood up and walked in front of Lu Zhou: "If a calculation has violated basic common sense, then there is a high probability that something is wrong with it." ”

Lu Zhou did not deny her claim.

"Maybe you're right, because I think so too. However, rather than whether the solution of the 3D NS equation has global regularity at a particular point, I want to know why? ”

After a pause, Lu Zhou, who was staring at the lake, continued.

"Why did our equation explode?"

……

"Explosion" can also be called divergence in the field of computational fluid dynamics, and some authors in many foreign literature like to use the word "blo-up" to describe this headache phenomenon.

Mathematically, it refers to many problems, such as the denominator of the process 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 point in space, the fluid flow velocity is getting faster and faster, and then the velocity tends to infinity, which is beyond the common sense in reality.

Lions et al. proved 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. However, there is still no unified conclusion in the academic community as to what is the NS equation in the three-dimensional case.

The general view in the mathematical community is that the solution of the NS equation in the three-dimensional case is optimistic about the existence and smoothness of the solution. Of course, the stock problem agrees with this point - otherwise, wouldn't the phenomenological models they built based on experimental data be tantamount to explaining lies with lies?

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

The feeling of hot water running down his head calmed down the impetuousness in his heart a lot.

The idea of indirect proof through abstract bilinear operators may be problematic, and instead of dwelling on uncertain problems, it is better to prepare for both, such as trying an additional way of thinking.

This kind of game, which challenges the pinnacle of the human mind, has no fixed solution in itself.

Before the Calabi conjecture was solved, the differential geometry community never imagined 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.

Maybe he will be able to discover something greater in it while solving the NS equation?

When he returned to his study, he turned on his computer and began to search for literature on the NS equation.

After all, it is a problem of the century rewarded by the Clay Institute, and the NS equation has a pivotal position in the field of partial differential equations, so scholars in the field of partial differential equations have also made a lot of beautiful research results around this equation.

Whenever research hits a bottleneck, Lu Zhou will try to find the piece of the puzzle that he lacks by retrieving papers from the database.

Just as Perelman immediately applied this method to solving the Poincaré conjecture after seeing Hamilton's paper on understanding the Ricci flow singularity, he was looking for something similar.

However......

Finding this piece of the puzzle is obviously not that simple.

Outside the window, the sunset was already covered with stars, and the hour hand of the clock on the wall had passed 12 o'clock and began to shift towards 1 o'clock.

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

The erratic thoughts in his mind, one moment like almost frozen ink, the other turned into a divergent column of smoke, which was a headache.

However, in this vague moment, a hint of realization suddenly appeared in Lu Zhou's heart.

"If you don't have ......tools, why don't you build your own?"

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

This seems to make a "simple" problem even more "complex".

But it seems to ......

Does it work?

The eyes are getting brighter and brighter.

Grabbing the glimmer of inspiration in the dark, Lu Zhou quickly grabbed a ballpoint pen and wrote a line of words on the paper.

【Lu Manifold】

Then, the pen in his hand couldn't stop......

……

When immersed in a job, time always flies.

In the blink of an eye, it's April.

For more than a month, Lu Zhou, who locked himself in the house, also spent a short and monotonous spring break.

And during this time, except for Vera who came to his house once and sent him a teaching report for this time, Lu Zhou almost cut off communication with the outside world.

In fact, although he asked Vera to send those things, he left them in the corner of his study after they were delivered, and barely turned them over.

At Princeton, Professor Lu's unique way of delving into problems is almost an anecdote that even recent undergraduates have heard of from older students.

Perhaps knowing that his research had entered a critical period, Professor Feverman was also considerate not to disturb him, but temporarily suspended his regular exchange meetings and began to conduct independent research separately and simultaneously.

And now, those efforts are finally bearing fruit.

Stopping the pen in his hand and looking at the stack of scratch paper in front of him, the corners of Lu Zhou's mouth hooked up a smile.

Lu Zhou, who had finally relaxed the taut strings in his head, began to think of something inconsequential.

For example, the name Lu manifold, is it a little unpleasant?

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

After thinking about it, Lu Zhou felt that it was better not to embarrass the candidates of the future generations.

The former seems prone to strange ambiguity, while the latter is unpleasant to read.

"The Chinese name is called Lu's manifold, and the English translation name is L manifold, referred to as L flow!"

Much more satisfied with the name, Lu Zhou casually changed the title on the manuscript paper, and then stacked the paper and put it in the corner of the table, preparing to sort out the contents one by one on the computer.

Just as he turned on the computer and was about to start this work, a string of bubbles suddenly popped up in the job bar in the lower right corner of the screen.

Xiao Ai: [Master, there's a new email!] (๑•̀ㅂ•́)و✧】

Seeing this message, Lu Zhou casually clicked on the link thrown by Xiao Ai and logged in to the mailbox.

The email was from the Annals of Mathematics.

As for the content, of course, it is the paper about the proof of Kakutani's conjecture.

From the beginning to the end of the email, a smile appeared on Lu Zhou's face again.

Although it was expected, he was sincerely happy for his students after seeing the email.

According to the decision of the editorial board of the Annals of Mathematics, their papers will be published in the most recent issue of the journal and will be tested by the entire mathematical community......