Put pen to paper, point to sentence.

Xu Chuan looked at the equation on the desk, with a smile on his face full of satisfaction.

The problems that he had pursued in Princeton for years in his previous life were met in this life.

The significance of the NS equation to the mathematical and physical circles and even the whole world is most perfectly explained at this moment.

The airliner flying in the sky does not suddenly disintegrate, the calm earth does not collapse on its own, and the diffusion effect of the fluid is perfectly restrained at this moment.

It is the mystery of the universe and the pinnacle of the human mind.

Of course, this is his glory!

When Xu Chuan began to study the last step of the NS equation in retreat, the video of his previous impact on the NS equation in the NTU class gradually spread to the entire mathematical and physical circles.

There are ongoing discussions in relevant professional forums and on campus websites.

After all, it is the problem of the century that has been rewarded by the Clay Institute, and the NS equation itself has a pivotal position in the field of partial differentiation.

Mathematicians in the field of partial differential equations have also done a lot of research around this equation, and it is no exaggeration to say that this is a hen that lays golden eggs.

It's just that it may end up in the hands of that Professor Xu today.

[, Professor Xu is making a move again! ] This time the goal is the last step of the NS equation! 】

【？？？？ 】

[What the hell, it's not April Fool's Day this year. 】

[Isn't it, he does research so quickly?] I remember that he only advanced the NS equation to a new level in the first half of this year, right? This kind of problem of the century, how many years can it be solved? 】

[Hemp egg! I have only written the beginning of my graduation thesis for a year, and Kawajin has already rushed to solve the NS equation? 】

[Hiss~, if he solves the NS equation this time, then he will kill two of the seven millennial problems alone, is it so terrifying? 】

[The NS equation is impossible to solve, and the top mathematicians who have hit this problem are not a thousand but eight hundred, but now it is still standing there majestically, and the singularity is not differentiable, and the NS equation is destined to be unsolvable! 】

[If you can't solve it, Professor Xu can't solve it? He has already solved one of the seven millennial problems, and this time it is estimated that it is only a matter of time. 】

[Anyway, it's mid-November now, and it's almost a month since those videos, is Professor Xu still researching?] Whether you can or not, come out and squeak. 】

From mid-October to mid-November, even after nearly a month, the relevant discussions are still very hot on the Internet.

A lot of people are looking forward to the end result.

The CMI official solution to this problem given by the Clay Institute of Mathematics in the United States is:

[Prove or no, for a given initial velocity vector field, whether the three-dimensional unsteady Navier-Stokes equation will blow up]

This is not only about the million meters of gold, but also about the development of fluid mechanics.

If the solution of the NS equation proves to be present and smooth, fluid mechanics will advance by leaps and bounds.

If the solution of the NS equation is proved to be non-existent, the development of fluid mechanics will probably suffer a great setback for a long time to come.

If there is no smooth solution to the NS equation, the frontier of fluid mechanics may follow the equation and cannot find a future boundary, or even worse, it may explode directly.

Of course, the mathematical community generally believes that the NS equation in the three-dimensional case has existential and smooth solutions, not only because fluid mechanics and partial differential equations have developed to this day, which have involved all aspects of mathematics.

It is also because there are many mathematicians who have made a lot of results based on this equation, which have been confirmed to be true, but the final answer is no, which always gives people a sense of unreality.

Just when the Internet was discussing how long it would take Xu Chuan to solve the final step of the NS equation, a paper quietly appeared on the Arxiv preprint website.

"Proof of the existence and smoothness of the solution of the three-dimensional incompressible Navier-Stokes equation." 》

A thesis that quickly made waves on Arxiv.

Because of the pre-fermentation, many mathematicians and physicists, and even scholars who didn't read this preprint website like arxiv before, have registered accounts to follow Xu Chuan.

The academic community knows that this big guy has the habit of throwing papers on arxiv before submitting them, so in order to get the progress related to the NS equation as soon as possible, everyone who received a message from the website squeezed into arxiv in a honeycomb.

[, Professor Xu uploaded the paper!] 】

[What paper?] 】

[What else can there be besides the proof of the NS equation!] 】

【？？？？ Is the real proof out? 】

[Ghost knows, I can't read it anyway, maybe it's scribbled? 】

[Ask for papers!] Has anyone downloaded the paper? Arxiv was paralyzed, and I couldn't even get in. 】

[Together!] 】

[To put it bluntly, it's useless for you to ask for it, it's better to honestly follow the blogs or tweets of those math masters, such as Tao, he will definitely express his opinion. 】

[It's terrifying, it looks like it might be real this time.] 】

[Heh, I still say that there can be no smooth solution to the NS equation! Even if Professor Xu proves it, it must be proved or not! 】

[Ah, yes, yes, yes, you're right! I would like to ask you about your old man's academic qualifications? 】

[Dog head, don't ask, ask is a civil science. 】

The sudden torrent squeezed arxiv pre-printed this website directly to stop eating.

Even the Los Alamos National Laboratory, which operates the servers, quickly added backup servers.

Relative to the additional spare server resources, more people flocked to the Arxiv website because of the NS equation.

The surge in traffic instantly shut down the entire site, and those scholars who reacted in hindsight saw nothing but a blank slate.

As a result, many people began to seek papers in other places.

The last step of the NS equation is not only a reward of one million meters of gold for the Clay Institute of Mathematics, but also a problem of the century related to the progress of fluid mechanics.

Even if you can't read it, you have to see what the paper looks like first, right?

What had been a lot of discussion that had subsided over time became heated again with a paper in Arixv.

Not only netizens who are talking about eating melons on the forum and the Internet, but also many well-known scholars in the field of mathematics and physics have expressed their concern about the proof paper of the NS equation uploaded by Xu Chuan.

University of California, Los Angeles.

Tao Zhexuan, who had already prepared to explain, quickly took over the downloaded and printed paper from his assistant.

Ever since he saw the mathematical tools built on microfluids in the mathematical physics system more than a month ago, he has been looking forward to this day all the time.

A new mathematical tool, the temptation for a man like him is too great.

Impatiently, he opened the paper and read it intently.

Based on micro-element fluids, the concept of mathematical sets is introduced, combined with manifolds, and Ricci manifolds are used to develop fluid topology and geometry."

Staring at the paper, Tao Zhexuan couldn't stop talking to himself excitedly.

Just as he expected, the equations on those three blackboards were a mathematical tool! A mathematical tool that combines the three fields of differential geometry, topology, and partial differential equations!

Even though he was called an all-round mathematician, he never imagined that there would be such a way to circumvent the limitations of the NS equation, which was unprecedented.

Yes!

Prior to that, he had also studied the NS equation.

In 15 years, he constructed an equation that was close to equivalence to the original NS equation and proved that this equivalent equation would emit in a finite time.

If one follows his train of thought and logic, it can be similarly inferred that the original NS equation will also explode in a finite time.

Although he believed that the smooth solution of the NS equation was real, he personally pushed it in the direction of the unsolvable.

This was also something that made him quite depressed, and it was not until the first half of this year, after the creator of the paper in his hand had taken the NS equation a big step forward, that he resumed working on the NS equation.

After reading the paper in his hand carefully, Tao Zhexuan closed his eyes and savored it.

To be honest, the paper in his hand was more 'excellent' than any paper he had read before.

The writing and ideas of the whole paper are as flawless as if they were made in nature.

In particular, the ingenious mathematical methods used in the paper made him can't help but praise them in his heart.

After quietly reminiscing about it, Tao Zhexuan couldn't wait to turn on the computer and log in to his blog.

His blog has been publishing all sorts of math-related content for a long time.

As a 'little bit of everything', he is involved in a wide range of mathematical fields, so his blog has also become a gathering place for many scholars who pay attention to the frontier fields of mathematics.

[The paper has already been read.] First of all, I would like to exclaim: "This is a perfect paper, so perfect that it even makes me feel that it is not written by man, but by God." ”】

[OK, back to the topic, Professor Xu's proof of the NS equation published on arxiv uses a new mathematical tool, my previous guess is not wrong, more than a month ago, he wrote the equation on the three-sided blackboard, it is to create a new mathematical tool!] 】

[This mathematical tool is based on microfluids, introduces the concept of mathematical sets, combines manifolds, and uses Ricci manifolds to develop fluid topology and geometry. Combine the mathematical knowledge of differential geometry, topology, and partial differential equations. 】

[It is foreseeable that in the future, this mathematical tool that has not yet been officially named will be as popular as the 'algebraic cluster and group mapping tool' created by Professor Xu when he proved Hodge's conjecture!] 】

[Therefore, I suggest that Professor Xu give him a good name, not like a tool for computational astrophysics, directly hanging 'extended application', which is really too annoying]

[Oh, yes, and one last point. 】

[If I were to give my opinion on this paper, there is no doubt that he succeeded!] 】

ps: The first update is delivered, and there is still in the evening. Ask for a commuter pass!

Thank you for the reader's big guy don't talk nonsense if I don't understand (200), book friend 20220519133742404 (100) for the reward, thank you, big guy.

(End of chapter)