Princeton Institute for Advanced Study.

Professor Feverman is talking to him in his office about mathematics in partial differential equations.

In recent months, in order to study the last step of the NS equation, he has been working hard for the second spring of old age, not to mention the NS equation every day, and has also pushed off most of the work in his hands.

It can be said that the last step of the NS equation is a must-have.

The two were communicating, and suddenly, the mobile phone that Deligne put on the table vibrate, and he picked it up subconsciously and looked at it, his brown-green pupils contracted slightly.

Immediately after, he unlocked his phone without hesitation and clicked on the message.

On the other side, Feverman stopped talking, looked at the friend with curiosity, and asked, "What's wrong?" What happened? ”

He knew his friend's personality very well, and he couldn't go to see something else without the important thing he was talking to.

Deligne didn't reply immediately, he went through the news in his hand before slowly raising his head and looking at Feverman, with a hint of hesitation and pity in his eyes.

"Perhaps, you don't have a chance."

"What's no chance?" Feverman looked confused, he didn't understand what Deligne was talking about.

"NS equation."

FEVERMAN: "???? ”

Deligne hesitated, but forwarded the message on his phone to him.

"I sent you the news, you better take a look."

With a question mark on his face, Feverman reached out of his pocket and unlocked the screen.

The first thing that caught his eye was the message that Deligne had sent him.

"Professor Xu Chuan has solved this millennial problem by attacking the last step of the NS equation in the class of NTU!"

The title of the message made Feverman's heart beat suddenly, and with incredulity in his eyes, he quickly clicked on the message and entered the details.

After a long time, Peverman raised his head and looked at his friend with a complicated expression.

"Maybe, I really don't have a chance."

Deligne shrugged his shoulders and did not speak.

With his knowledge of his student, if he had started working on a certain problem in earnest, he would probably not have succeeded.

And judging from the equations on the pictures attached to the message, I am afraid that he already has some ideas about how to solve the NS equation.

Perhaps, after a while, they will see that the NS equation is completely solved.

This is of great significance to the world of mathematics, physics and industry.

Honestly, he's looking forward to it!

It's just a pity that his friend is gone.

Since the beginning of the cooperation with Xu Chuan on the NS equation, he has always been one step slower, from two phased achievements to the last step now.

If the opponent was someone else, his friend might still be able to fight.

But met him that student

Thinking about it, Deligne couldn't help but shake his head.

Perhaps, Feverman will have a chance to fight if he is thirty or forty years younger, but now, I am afraid there is no chance.

On the other side, Huaguo, Jinling.

Xu Chuan didn't pay attention to these news on the Internet, and even if a media reporter wanted to interview him, he was stopped by Zheng Hai.

Since returning from the classroom, he has locked himself in his study and begun to work on the last step of the NS equation with all his might.

To be honest, he never imagined that the study of the NS equation would come so soon.

Because before that, he had almost come to the end of his road of proving the phased results of the NS equation using Kolmogolov's K4 theory.

When the viscosity coefficient ν tends to zero, the solution of the initial boundary value problem of the Navier-Stokes equation, whether it tends to the solution of the corresponding ideal fluid in the interior of the fluid motion region, the description of the fluid boundary layer problem, and the fact that the fluid flow velocity is getting faster and faster in three-dimensional infinite space, and then the velocity tends to infinity, which is beyond the common sense in reality.

This step is both the last step and the hardest part.

Until the correct answer is found, the existence of a smooth solution to the three-dimensional incompressible Navier-Stokes equation is still a mystery, and no one knows whether the divergence of turbulence will eventually calm down.

Otherwise, when Fepferman invited him, he would not have directly refused.

It's just that Xu Chuan didn't expect that only five or six months had passed, and new inspirations and paths would come so quickly.

A trip to basic mathematics class brought him a new way of thinking.

If each fluid emission microfluidic unit is considered a mathematical value, then using microfluid mathematics he can construct a set of these numbers.

In Poincaré's conjecture or Poincaré's theorem, any single-connected, closed three-dimensional manifold must be the same as a three-dimensional sphere.

To put it simply, a closed three-dimensional manifold is a bounded three-dimensional space; And single connection means that each closed curve in this space can be continuously contracted into a point.

In other words, in a closed three-dimensional space, if each closed curve can shrink to one point, this space must be a three-dimensional sphere.

Using microfluids, he built a mathematical tool to encompass all the fluid diffusion in the NS equation into a set, and then used the Ricci manifold to expand the fluid topology and construct the geometry from an irregular manifold to a regular manifold.

This path spans the most basic micro-element fluids, complex diffusion fluids, and ultimate turbulent fluids, and finally successfully constructs a new mathematical tool.

A new path, a new tool, is the answer he handed in in the last step of the NS equation.

This is completely different from using mathematics and practical physics to climb the NS equation before.

This time, he followed the path of pure mathematics.

Twisting and turning, climbing for a long time, and returning to the original point.

However, there is no fixed solution to the NS equation, which is one of the seven millennial problems that challenge the pinnacle of the human mind.

Although in the past, mathematics was often used as a tool to solve difficult problems in physics, it has never been stipulated that physics should not be used as a tool to solve mathematical problems.

For this kind of problem standing at the pinnacle of humanity, as long as you can take a step forward, even if it is a centimeter by millimeter, no matter what method is used, it is worth it.

In the study, Xu Chuan looked at the manuscript paper on the desk.

The tools to cross the abyss are already available, and all that remains is to complete the summit.

If the NS equation is compared to a towering snow-capped peak, he had climbed halfway up the mountain before that. But it was stopped by an abyssal rift.

The tools he had used to climb the snowy peaks were not enough to support him across this bottomless abyss, but now, after making a circle halfway up the mountainside, he miraculously found a forest in the col.

Cut wood, build bridges, and cross the abyss little by little.

The mathematical tools derived from microfluids are the bridge to conquer the final step of the NS equation.

With the help of this tool, he can finally continue to move towards the peak.

After sorting out the manuscript paper on his desk, he pulled out a new stack of A4 paper from the drawer and laid it out in front of him.

He picked up his pen and wrote the last title on the paper.

[Proof of the existence and smoothness of the solution of the three-dimensional incompressible Navier-Stokes equation!] 】

It's time to make your way to the final summit!

I don't know how long it has been, but time seems to have paused in this small study.

For Xu Chuan, the pen in his hand has never stopped since he wrote that title.

Finally, when the last line quietly jumped onto the white manuscript paper, a smile of satisfaction appeared on his lips.

It's time to give the final conclusions.

With a smile, Xu Chuan gently moved his palm, allowing the pen in his hand to lower down a position.

【. When the viscosity coefficient ν tends to zero, the solution of the initial boundary value problem of the Navier-Stokes equation tends to the corresponding ideal fluid state in the fluid motion region. That is, there is a solution to the initial boundary value of the Euler equation! 】

[To sum up all the inferences, we can easily know that in the three-dimensional incompressible Navier-Stokes equation, the solution exists!] And smooth! 】

PS: Ask for a monthly pass! It's time to give me your monthly pass! φ(｀ω)。

Thanks to reader Mota Mota, starting point reading (5000) big guy book friends 20220519133742404 (100), elfhunter (100), Yipeeee (100) for the tip.

Thank you, big guys, thank you

(End of chapter)