Great Country Academician

In the auditorium, there were no seats, and there was a lot of voices.

Stirring figures and whispered discussions gathered together.

It was not only the scholars in the auditorium who came to participate in the exchange report that were lively. Backstage in the auditorium, the teachers and staff of Nantah's Administrative Office are also busy doing the final inspection.

From microphone to projection, from sound to projection, all equipment during the exchange meeting must be guaranteed to be free of any problems.

Although they are not on stage to give academic reports.

But to be honest, they were more nervous than that.

After all, this is the world's top academic exchange meeting in front of you, with more than 3,000 scholars present.

And there are a large number of top mathematicians and top physicists in it.

For the academic community, even if it is placed internationally, such a grand event may not be held once every few years.

On the other side, Xu Chuan sat quietly on a chair in formal attire and waited for the start of the exchange meeting.

For him, such a scene is not unfamiliar, even he is used to it.

Soon, a staff member trotted over and said with admiration, "Professor Xu, it's already 8:55, do you see?"

Xu Chuan nodded, stood up and said, "Thank you."

After tidying up his clothes and smoothing out the wrinkles, he walked towards the front desk.

Although the report will start at nine o'clock, as the speaker, he came to the stage a little earlier to show respect and etiquette to the scholars who came to participate in the report.

When Xu Chuan walked slowly onto the podium, all eyes in the auditorium were cast on him.

There is no need for anyone to maintain discipline. When he appeared on the stage, the auditorium, which was noisy and chaotic due to discussions, became quiet in an instant, and even the sound of breathing could not be heard at this moment.

Standing on the reporting platform, Xu Chuan looked down at the audience.

The big screen behind him and the synchronous projection equipment installed around the auditorium were turned on at the same time, and a line of clear titles emerged from the silver-white curtain.

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

A line of black block letters jumped into everyone's eyes.

Of course, considering that most of the scholars present are international scholars, there is also a line of English under the block letters.

Looking at the expectant eyes under the stage, Xu Chuan took a deep breath and spoke slowly.

"First of all, welcome to everyone who came to participate in the exchange report, and thank you for taking time out of your busy schedule to come here to listen to my academic report."

"Today's exchange report, as you can see, is a proof of the existence and smoothness of the solution to the NS equation."

After a pause, Xu Chuan didn't go directly to the topic as before. He changed the topic, and then said, "Before officially starting the report meeting, I want to add some digressions."

"Of course, it's also related to the NS equation."

"In the past, we have harvested countless formulas, including the familiar mass-energy equation, Newton's second law, Maxwell's equations, Euler's formula, 1+1=2, NS equations, etc."

"Each of them drives our civilization and science forward."

"Just like the mass-energy equation, it can be said to be one of the most concise physical formulas, but it is one of the deepest mysteries in the universe. Through the study of it, we have revealed the nature of light and found a ruler to measure the universe. I also know the conservation of mass and energy”

"For example, through the study of Maxwell's equations, we can use the grid to transmit and use electric energy quickly and efficiently; we can use radio waves to transmit information efficiently and widely."

"And in the NS equation, there is also such a profound and secret meaning hidden."

"It's just that, for a long time, our research on it has not been able to understand the essence."

"Even in the nineteenth century, we have already summed up a set of methods and equations to induce the laws of fluid motion."

"But to this day, we still have a superficial understanding of the deeper mathematics, physics and motion behind this set of methods and equations."

"Like a high-speed flying aircraft, limited by the accuracy and efficiency of the numerical solution of the NS equations, we still need to rely on a large number of experiments in the wind tunnel for its shape design, and the numerical solution cannot completely replace the wind tunnel experiment so far."

"Why doesn't the airliner flying in the sky disintegrate suddenly? Why doesn't the peaceful land collapse by itself? What is the diffusion effect of the fluid that constrains it?"

"All this was mysterious and unknown to us in the past."

"But today, it's time to give them answers!"

After the opening remarks, Xu Chuan pressed the control pen in his hand, and the projected PPT copy turned over a new chapter.

"OK, the digression is over, and now we are officially entering the topic."

"I believe that everyone here has read my thesis before coming here. As for the proof in the thesis, I will not repeat it completely."

"In today's report meeting, the focus of my explanation will be on the key nodes of proving the NS equation and the new mathematical tool 'micro-element construction method' used."

"I also believe that you should be interested in these things."

"Not much to say, let's enter the report."

"The incompressible Navier-Stokes equation describes the motion of a viscous incompressible homogeneous fluid. According to the mass conservation and momentum conservation in Newton mechanics, we get the following equation:

[tuνu +(u )u =p + f, u =n∑i=1iui = 0]

As Xu Chuan began to officially enter the report, the audience in the audience gathered their spirits, stared at the curtain closest to them with full attention, and their eyes fell on the reflected pictures and calculation formulas.

Everyone is listening carefully, unwilling to let go of any detail, unwilling to miss any moment.

".Generally speaking, the derivation of the NS equation is to analyze the force of the fluid micro-cluster. We can not make any assumptions about the fluid. Then μ, density, etc. will also have partial derivatives for the three directions. Equation It's going to be very complicated."

【3∑i=1（xi(H(φ)φxi)= 0）.】

".The flow after the shock wave is described by irrotational flow. By introducing the potential function φ, Euler's equations can be simplified into a second-order nonlinear partial differential equation, called the potential flow equation."

"."

On the podium, Xu Chuan held the control pen in his hand, looked at the projection screen and explained the key proof steps of the NS equation in a calm and orderly manner.

For solving fluid problems, both the Euler method and the Lagrangian method are necessary.

The Euler method describes the velocity and force of each point in Euclidean space, but the fluid particles corresponding to the point may change; while the Lagrangian method tracks each fluid particle.

These two methods were one of the most commonly used methods used by mathematicians to study NS equations and fluid mechanics in the past, and he didn't need to explain them too much, so Xu Chuan took them directly.

And the next step is to prove the key point of the NS equation process!

Based on the micro-element fluid in the mathematical physics system, the concept of set is introduced, and differential equations, topological geometry and partial differential equations are integrated.

This is the key tool for him to prove the NS equation, and it is also the core point for introducing the concept of topological geometry into differential equations and partial differential equations.

In the auditorium, Terence Tao sat beside Deligne, listening to the report carefully.

And when the 'micro-element construction method' appeared, he sat up straight and stared at the screen tightly.

Following Xu Chuan's explanation, his eyes also danced with a bright light, and the trace of doubt that he had originally gradually dissipated with the voice on the podium.

"So that's it, he's really a genius monster!"

After understanding all the key points, Tao Zhexuan leaned gently on his back, and spit out from his mouth with a sound of sudden realization and exclamation.

On the side, after hearing his voice, Deligne replied with a smile: "Compared to me, he is already better than blue than blue."

Hearing this, Tao Zhexuan looked over curiously, and asked, "Why do I feel that you have understood everything about this paper before the report meeting?"

Deligne smiled and said, "If you had participated in the European mathematics exchange meeting half a month ago, you could have understood it before the report meeting."

Tao Zhexuan frowned slightly and asked, "Professor Xu has gone too?"

Deligne shook his head and said, "No, he didn't go, but after his thesis was uploaded on arxiv, we came here from Europe together."

Hearing this, Tao Zhexuan suddenly understood, and said with a hint of envy: "So, it seems that you have gained a lot from the exchange, and I missed it."

He knew about the exchange meeting in Europe, but he didn't go.

If he had known that these people would come directly here to communicate in advance, he would have come to join him no matter what.

This kind of academic exchange among many top mathematicians is really rare.

Especially for people like him who want to go further academically.

On the podium, Xu Chuan's report continued.

".Using standard energy calculations we can obtain the consistency of v, independent of time, and by proving the uniform boundedness of θhetaθ, the following equation can be obtained:"

[∫T0max(x∈[0,1])|θ^1/2(x,t)-∫T0θ^1/2(x,t)dx|dt≤C]

Thus, it can be proved that the norm of θ－L∞(0, ∞; L p ) is bounded, and at the same time, use this equation.

Following Xu Chuan's narration, the "micro-element construction method" was gradually introduced into the proof of the last step of the NS equation.

For the problem of the overall existence of the smooth solution of the three-dimensional incompressible Navier-Stokes equation, it is like a space elevator in a science fiction novel, from the earth to space, the whole process is very clean and neat, without any excess.

And with the passage of time, the ending process was officially spit out from Xu Chuan's mouth.

In the auditorium, the quiet atmosphere was slowly filled with various emotions such as anticipation, confusion, tension, and stunned.

Sitting next to Witten, Roger Penrose poked Edward Witten beside him with his hand, and asked with seriousness and doubt in his eyes.

"Do you understand?"

To be honest, he didn't understand much of the whole report, perhaps less than half of it?

After all, he is a theoretical physicist who studies things like gravitational collapse, space-time singularities, and black holes.

Even some achievements in mathematics are limited to areas such as geometry and abstract structures.

For the knowledge in fields such as topology and partial differential equations, although those who study physics basically know a little, they basically only know a little.

It is basically impossible to use it to study advanced and cutting-edge mathematics.

So halfway through hearing it, especially when the so-called "micro-element construction method" was introduced, he began to feel a little confused.

Sitting next to him, after hearing the question, Edward Witten replied without turning his head: "It's okay."

His ability in mathematics is not comparable to that of Penrose. He specializes in several areas of mathematics including quantum field theory, string theory and related topology and geometry.

Although NS equations were outside his scope, many of the methods used by his student were topological.

Hearing this, Roger Penrose frowned, feeling a little pricked. He is also a mathematical physicist, but he actually understood?

After thinking about it, he asked, "Then do you regret it?"

Hearing this, Wei Teng, who was listening to the closing report, twitched involuntarily.

This man is so annoying!

PS: There is another chapter tonight, ask for a monthly pass!