Chapter 321 Answers to the Millennium Puzzle!
Put pen to paper, click a sentence.
Xu Chuan looked at the calculations on his desk with a smile on his face, full of satisfaction.
The problem that I had been pursuing for several years at Princeton in my previous life was finally satisfied in this life.
The significance of the NS equation to the world of mathematics, physics, and even the entire world is most 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 is most perfectly constrained at this moment.
It is the mystery of the universe and the pinnacle of the 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 retreat, the video of him impacting the NS equation in the NTU class gradually spread to the entire mathematics and physics circles.
Discussions continue in relevant professional forums and campus websites.
After all, it is the problem of the century that is being rewarded by the Cray Institute, and the NS equation itself plays a pivotal role in the field of partial differentials.
Mathematicians who study partial differential equations have also done a lot of research on this equation. It is no exaggeration to say that this is a hen that can lay golden eggs.
It's just that it may end in the hands of Professor Xu today.
[Damn it, Professor Xu struck again! The goal this time is the last step of the NS equation! 】
【? ? ? ? 】
[What the hell, this isn’t April Fool’s Day. 】
[No, is he doing research so quickly? I remember that he only pushed the NS equation to a new level in the first half of this year, right? This kind of problem of the century can be solved in a few years? 】
【Damn it! I have been working on my graduation thesis for a year and I have only written the beginning. Is it true that the solution to the NS equation exists? 】
[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 not even 1,000 to 800 top mathematicians who have tackled this problem, but now it still stands there motionless. The non-differentiability of singular points means that the NS equation is doomed to have no solution! 】
[You can’t solve it because Professor Xu can’t solve it? He has already solved one of the Seven Millennium Puzzles, and this time it is probably only a matter of time. 】
[By the way, it’s already mid-November, and it’s been almost a month since those videos. Is Professor Xu still working on it? Regardless of whether you can or not, just come out and say something. 】
From mid-October to mid-November, even though nearly a month has passed, related discussions are still very popular on the Internet.
Many people are looking forward to the final result.
The official solution to this problem given by CMI, the Clay Mathematics Institute of the United States, is:
[Prove or disprove whether the three-dimensional unsteady Navier-Stokes equation will blowingup for a given initial velocity vector field]
This is not only related to the one million meters of gold, but also related to the development of fluid mechanics.
If the solution to the NS equation is proven to exist and be smooth, fluid mechanics will advance by leaps and bounds.
If the solution to the NS equation is proven not to exist, the development of fluid mechanics may suffer great setbacks for a long time to come.
If there is no smooth solution to the NS equation, the frontier field of fluid mechanics may diverge along with the equation and find no future boundaries, or even more seriously, it may directly explode.
Of course, the mathematical community generally believes that the NS equation in the three-dimensional case has existential and smooth solutions, not only because the development of fluid mechanics and partial differential equations to this day has involved all aspects of the field of mathematics.
It’s even more because many mathematicians have made numerous results based on this equation, all of which have been confirmed to be true, but if the final answer is no, it always gives people an unreal feeling.
While the Internet was 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.
"On the three-dimensional incompressible Navier-Stokes equation, the proof of the existence and smoothness of the solution." 》
A paper quickly made waves on Arxiv.
Because of the advance fermentation, many mathematicians and physicists, and even scholars who had not seen preprint websites like arxiv before, have registered accounts and followed 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 related to NS equations as soon as possible, everyone who received the website message prompts crowded into arxiv. .
[Shit, Professor Xu uploaded the paper! 】
[What paper? 】
[What else can there be besides the proof of the NS equation! 】
【? ? ? ? Is the real evidence out? 】
[Who knows, I can’t understand it anyway. Maybe it’s written randomly? 】
[Requesting a paper! Has anyone downloaded the paper? arxiv is paralyzed and I can't even enter. 】
【Same request! 】
[To put it bluntly, it’s useless for you to beg. You should just follow the blogs or Twitter of those math masters, such as Tao, who will definitely express his opinions. 】
[It’s so scary. It seems like it might be true this time. 】
[Oh, I still say the same thing, NS equations cannot have smooth solutions! Even if Professor Xu proves it, he must not prove it! 】【Ah, yes, yes, yes, everything you said is right! I would like to ask you about your educational background? 】
[Gotou, don’t ask, asking is just civil science. 】
The sudden torrent was so crowded that the arxiv preprint website stopped immediately.
Even Los Alamos National Laboratory, which operates the servers, quickly added backup servers.
Compared with the increased spare server resources, more people flocked to the Arxiv website because of the NS equation.
The sudden increase in visits brought the entire website to a standstill, and those scholars who reacted with hindsight saw only a blank space.
So many people began to seek papers in other places.
The last step of the NS equation is not only related to the reward of one million meters of gold from the Clay Mathematics Institute, but also a century-old problem related to the progress of fluid mechanics.
Even if you don’t understand it, you still need to see what the paper looks like first, right?
The discussion that had gradually subsided over time became extremely intense again with a paper on Arixv.
Not only netizens who discuss eating melons on forums and on the Internet, but also many well-known scholars in mathematics and physics have expressed concern about the proof paper of the NS equation uploaded by Xu Chuan.
University of California, Los Angeles, California, USA.
Tao Zhexuan, who had already prepared his explanation, quickly took the downloaded and printed paper from his assistant.
Ever since he saw the mathematical tools built based on microfluid in the mathematical physics system more than a month ago, he has been looking forward to this day all the time.
A brand-new mathematical tool, the temptation is too great for people like him.
Can't wait, he opened the paper and read it with concentration.
"Based on micro-element fluids, we introduce the concept of mathematical sets, combine it with manifolds, and use Ricci manifolds to develop fluid topology and geometric structures."
Staring at the paper, Tao Zhexuan couldn't help but excitedly muttered to himself.
Just as he expected, the calculations on the three blackboards were a mathematical tool! A mathematical tool that combines the three major fields of differential geometry, topology, and partial differential equations!
Even though he is known as an all-around mathematician, he has never thought that there is such a way to circumvent the limitations of NS equations. This is unprecedented.
Yes!
Before that, he had also studied NS equations.
In 2015, he constructed an equation that was nearly equivalent to the original NS equation, and proved that this equivalent equation would radiate in a finite time.
If you follow his ideas and logic, it can be similarly inferred that the original NS equation will also explode in a limited time.
Although he believed that smooth solutions to the NS equations existed, he personally pushed them towards the unsolvable direction.
This was also something that made him quite depressed. It was not until the first half of this year that the creator of the paper in his hand took the NS equation a big step forward that he started to study the NS equation again.
After eagerly reading the paper in his hand carefully, Tao Zhexuan closed his eyes and thought about it.
To be honest, the paper in his hands was 'better' than any paper he had ever seen before.
The writing and ideas of the entire paper are as flawless as if they were made in heaven.
In particular, he couldn't help but praise the ingenious mathematical methods used in the paper.
After thinking about it quietly, Tao Zhexuan couldn't wait to turn on the computer and log in to his blog.
A long time ago, his blog began to publish various mathematics-related content.
As someone who 'knows a little bit' about everything, he covers a wide range of mathematics fields, so his blog has become a gathering place for many scholars who pay attention to cutting-edge fields of mathematics.
[The paper has been read. First of all, I want to sigh: "This is a perfect paper, so perfect that I feel that it is not written by humans, but written by God."]
[OK, back to the topic. The proof of the NS equation published by Professor Xu on arxiv used a new mathematical tool. My previous guess was not wrong. More than a month ago, he wrote on the three blackboards. The calculation formula is creating a brand new mathematical tool! 】
[This mathematical tool is based on micro-element fluids, introduces the concept of mathematical sets, combines manifolds, and uses Ricci manifolds to expand fluid topology and geometric structures. It combines mathematical knowledge in the three fields 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 variety and group mapping tool' created by Professor Xu when he proved the Hodge conjecture! 】
[Therefore, I suggest that Professor Xu give him a good name. Don’t just say “expanded applications” like a tool for computational astrophysics. This is really annoying]
[Oh, yes, there is one last point. 】
[If I were asked to express my opinion on this paper, there is no doubt that he succeeded! 】
ps: The first update has been delivered, and there will be more in the evening. Asking for a monthly ticket!
Thanks to the readers, please stop talking nonsense if you don’t understand me (200), and the book friend 20220519133742404 (100) for the reward. Thank you, boss.
(End of chapter)