Xu Chuan looked at the calculations on his desk with a smile on his face, full of satisfaction.
The difficult problem that I had been pursuing for several years in 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 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 his previous impact on the ns equation in the NTU class gradually spread to the entire mathematics and physics circles.
Discussions continue on 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 an important role in the field of partial differentials.
Mathematicians who study partial differential equations have also made many research results around 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 at the hands of Professor Xu today.
[Damn it, Professor Xu strikes again! This time the target is the last step of the ns equation!]
【????】
[What the hell, this isn’t April Fool’s Day.]
[No, he does research so quickly? I remember that he only pushed the ns equation to a new level in the first half of this year, right? Such a century-old problem can be solved in just a few years?]
[Damn it! I’ve been writing my graduation thesis for a year and I’ve only written the beginning. Is God already running towards the existence of a 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 not even a thousand but eight hundred 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! 】
[Can’t you solve it if you can’t solve it with Professor Xu? He has already solved one of the seven millennium problems. It is probably only a matter of time this time. 】
[By the way, it’s already mid-November, and it’s been almost a month since those videos. Is Professor Xu still researching? Whether you can or not, please 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 the Clay Institute of Mathematics in the United States is:
[Prove or disprove, for a given initial velocity vector field, whether the three-dimensional unsteady nver-stokes equation will explode]
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 develop 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.
This is especially 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 rv preprint website.
"On the three-dimensional incompressible nver-stokes equation, the proof of the existence and smoothness of the solution."
A paper quickly made waves on rv.
Because of the advance fermentation, many mathematicians and physicists, and even scholars who had not seen preprint websites like rv before, have registered accounts and followed Xu Chuan.
The academic community knows that this big guy has the habit of posting papers to RV before submitting them, so in order to get the progress related to the NS equation as soon as possible, everyone who received the website message prompts crowded into RV.
.
[Shit, Professor Xu uploaded the paper!]
【What paper?】
【What else can there be besides the proof of ns equation!】
【????The real evidence came out?】
[Who knows, I can’t understand it anyway, maybe it’s scrawled? 】
[Requesting the paper! Has anyone downloaded the paper? The rv is paralyzed and I can’t even enter.]
【Same request!】
[To put it bluntly, your begging is of no use. 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 said that, the ns equation cannot have a smooth solution! Even if Professor Xu proved it, he must have proved it wrong!]
[Ah, yes, yes, everything you said is right! I would like to ask you about your educational background?]
[Gotou, don’t ask, it’s civil science if you ask.]
The sudden torrent was so crowded that the rv preprint website stopped immediately.
Even if Los Alamos National Laboratory, which is responsible for operating the server, quickly added backup servers, it was of no use.
Compared with the increase in spare server resources, more people flocked to the rv website because of the ns equation.
The sudden increase in visits brought the entire website to a halt in an instant, and those scholars who reacted belatedly 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 one million meter gold reward 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 discussions that had gradually subsided over time became extremely intense again due to a paper on rv.
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 micro-element fluids 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 is too tempting for people like him.
Unable to wait, he opened the paper and read it with all his concentration.
"Based on micro-element fluids, the concept of mathematical sets is introduced, combined with manifolds, and manifolds are used 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 integrated 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 the NS equation. This is unprecedented.
Yes!
Before that, 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 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 the smooth solution of the NS equation really existed, he personally pushed it 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, and he started to study the ns equation again.
After eagerly reading the paper in his hand carefully, Terence Tao closed his eyes and thought about it.
To be honest, the paper in his hand was 'better' than any paper he had ever seen before.
The writing and thinking of the entire paper are as flawless as if they were made in heaven.
Especially the ingenious mathematical methods used in the paper made him couldn't help but praise it in his heart.
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 contents.
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.
[I have read the paper. 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."]
[Okay, back to the topic, the proof of the ns equation published by Professor Xu on rv 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 exactly 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 manifolds to expand 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 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 before!]
[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. Please vote for me!
Thanks to the readers, if you don’t understand me, please stop talking nonsense (200), and the book friends (100) for the reward. Thank you, boss.
