Chapter 321 Answering the Millennium Question!

Put pen to paper and make sentences.

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

The difficult problem that he had pursued for several years in Princeton in his previous life was satisfied in this life.

The significance of the NS equation to the mathematical and physical communities and even the entire world was perfectly explained at this moment.

The passenger plane flying in the sky will not suddenly disintegrate, and the calm earth will not collapse on its own. The diffusion effect of the fluid was perfectly constrained at this moment.

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

Of course, this is even more of his glory!

When Xu Chuan began to study the last step of the NS equation in seclusion, the video of his impact on the NS equation in the classroom of Nanjing University gradually spread to the entire mathematical and physical communities.

There are constant discussions on related professional forums and campus websites.

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

Mathematicians studying partial differential equations have also made many research results around this equation. It is no exaggeration to say that this is a hen that lays golden eggs.

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

[Fuck, Professor Xu has made another move! This time the goal is the last step of the NS equation! ]

[? ? ? ? ]

[What the hell, isn't this April Fool's Day? ]

[No, is he doing research so fast? I remember that he only pushed the NS equation to a new height in the first half of this year? This century-old problem can't be solved in a few years? ]

[Damn it! I've been writing my graduation thesis for a year and I've only written the beginning, but Chuan Shen is already rushing to the existence of the solution to the NS equation? ]

[Hiss~, if he solves the NS equation this time, then he has solved two of the seven millennium problems by himself, is it so scary? ]

[The NS equation is impossible to solve. There are at least 800 top mathematicians who have challenged this problem, but now it still stands there motionless. The singularity is not differentiable, which means that the NS equation has no solution! ]

[If you can't solve it, Professor Xu can't solve it? He has already solved one of the seven millennium problems, so this time it's probably just a matter of time. ]

[It is already mid-November, and it has been almost a month since those videos were released. Is Professor Xu still researching? Whether you can or not, please come out and say something. ]

From mid-October to mid-November, even after nearly a month, the related discussions on the Internet are still quite popular.

Many people are looking forward to the final result.

The official solution given by the Clay Mathematics Institute (CMI) in the United States for this problem is:

[Prove or disprove whether the three-dimensional unsteady Navier-Stokes equations will blow up for a given initial velocity vector field]

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

If the solution of the NS equation is proven to exist and is smooth, fluid mechanics will develop by leaps and bounds.

If the solution of the NS equation is proven to not exist, the development of fluid mechanics may suffer a great setback for a long time in the future.

If there is no smooth solution to the NS equation, the frontier field of fluid mechanics may also diverge with the equation and find no future boundaries, or even more seriously, it may explode directly.

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

It is also because many mathematicians have made many achievements based on this equation, all of which have been confirmed to be true, and if the final ultimate answer is no, it always gives people a sense of unreality.

Just as people on the Internet were discussing how long it would take Xu Chuan to solve the last step of the NS equation, a paper quietly appeared on the Arxiv preprint website.

"Proof of the existence and smoothness of solutions to the three-dimensional incompressible Navier-Stokes equation."

A paper quickly set off a wave on Arxiv.

Because of the previous fermentation, many mathematicians and physicists, even scholars who didn't read preprint websites like arxiv before, registered accounts to follow Xu Chuan.

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

[Fuck, Professor Xu uploaded a paper! ]

[What paper? ]

[What else can it be except the proof of the NS equation! ]

[? ? ? ? Is it really proved? ]

[Who knows, anyway I can't understand it, maybe it's written randomly? ]

[Please ask for the paper! Has anyone downloaded the paper? Arxiv is paralyzed, I can't even get in. ]

[Same request! ]

[To be honest, it's useless for you to ask, you should just pay attention to the blogs or Twitter of those math masters, such as Tao, he will definitely express his opinions. ]

[It's really scary, it seems that this time it may be true. ]

[Hehe, I still say that the NS equation cannot have a smooth solution! Even if Professor Xu proves it, it must be a disproven! ]

[Ah, yes, yes, yes, you are right! I want to ask you about your education background? ]

[Don't ask, you are just a layman. ]

The sudden flood squeezed the arxiv preprint website and it was down.

Even if the Los Alamos National Laboratory, which was responsible for operating the server, quickly added backup servers, it was useless.

Compared with the few backup server resources added, more people flocked to the arxiv website because of the NS equation.

The surge in traffic instantly brought the entire website down, and those scholars who reacted late saw only a blank.

So many people began to ask for papers in other places.

The last step of the NS equation is related to the reward of one million dollars from the Clay Mathematics Institute, and it is also a century-old problem related to the progress of fluid mechanics.

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

The discussions that had gradually calmed down with the passage of time became extremely intense again with a paper on Arixv.

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

In the University of California, Los Angeles, California, USA.

Tao, who had already prepared for the explanation, quickly took the downloaded and printed paper from his assistant.

Since he saw the mathematical tools built based on the microfluid in the mathematical physics system more than a month ago, he has been looking forward to the arrival of this day all the time.

A brand-new mathematical tool, for people like him, the temptation is too great.

He couldn't wait to open the paper and read it attentively.

". Based on the microfluid, the concept of mathematical sets is introduced, combined with manifolds, and Ricci manifolds are used to develop fluid topology and geometric structure."

Staring at the paper, Tao was so excited that he couldn't stop talking to himself.

As he expected, the formulas on the three blackboards were a mathematical tool! A mathematical tool that integrates the three fields of differential geometry, topology, and partial differential equations!

Even though he was known as an all-round mathematician, he had never thought that there would be such a way to bypass the limitations of the NS equation, which was unprecedented.

Yes!

Before this, he had also studied the NS equation.

In 2015, he constructed an equation that was nearly equivalent to the original NS equation and proved that this equivalent equation would scatter in a finite time.

If we follow his ideas and logic, it can be inferred that the original NS equation will also explode in a finite time.

Although he believed that the smooth solution of the NS equation really existed, he personally pushed it in an unsolvable direction.

This was also a very depressing thing for him. It was not until the first half of this year that the creator of the paper in his hand took a big step forward in the NS equation that he started to study the NS equation again.

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

To be honest, this paper in his hand is more "excellent" than any paper he has ever read before.

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

Especially the clever mathematical methods used in the paper, which made him praise it constantly in his heart.

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

A long time ago, his blog began to publish various mathematical content.

As a man who "knows a little bit" about everything, he involves a wider range of mathematical fields, so his blog has also become a gathering place for many scholars who pay attention to the frontiers of mathematics.

[I have read the paper. First of all, I want to sigh: "This is a perfect paper, so perfect that it even makes me feel that it is not written by people, 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 was not wrong. More than a month ago, the formula he wrote on the three blackboards was creating a brand new mathematical tool! ]

[This mathematical tool is based on a microfluid, introduces the concept of mathematical sets, combines manifolds, and uses Ricci manifolds to develop fluid topology and geometric structures. It combines mathematical knowledge in the three major fields of differential geometry, topology, and partial differential equations.]

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

[Therefore, I suggest that Professor Xu give it a good name, and don't just call it "extended application" like the computational astrophysics tool, which is really annoying]

[Oh, by the way, there is one last point. ]

[If you want me to express my opinion on this paper, there is no doubt that he succeeded! ]

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