Chapter 327 Wei Teng: This Guy Is so Annoying!

In the auditorium, there were no seats, but the voices were bustling.

The moving figures and the whispering discussions gathered together.

It was not only the scholars who came to attend the exchange report meeting in the auditorium that were lively. In the backstage of the auditorium, the teachers and staff of the Political Affairs Office of Nanjing University were also busy doing the final inspection.

From microphones to projections, from sound to projection, all equipment must be ensured to have no problems during the exchange meeting.

Although they were not on the stage to give academic reports.

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

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

And there were many top mathematicians and top physicists in it.

For the academic community, even if it was put on the international stage, such a grand event might not happen once in a few years.

On the other side, Xu Chuan sat quietly in a chair in formal attire, waiting for the exchange meeting to begin.

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

Soon, a staff member trotted over and said with admiration: "Professor Xu, the time is already 8:55, what do you think?"

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

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

Although the lecture started at 9 o'clock, as a speaker, he went on stage a little earlier to show respect and etiquette to the scholars who came to participate in the lecture.

When Xu Chuan walked slowly to the podium, everyone in the auditorium looked at him.

No one was needed to maintain discipline. When he appeared on the stage, the auditorium, which was originally noisy and chaotic due to the discussion, became quiet in an instant, and even the sound of breathing could not be heard at this moment.

Standing on the podium, Xu Chuan overlooked the audience below.

The large screen behind him and the synchronous projection equipment installed in the auditorium were turned on at the same time, and a clear line of titles appeared on the silver-white screen.

[Proof of the existence and smoothness of solutions to the three-dimensional incompressible Navier-Stokes equations! 】

A line of black regular script characters caught everyone's attention.

Of course, considering that most of the scholars present were international scholars, there was also a line of English under the regular script Chinese characters.

Looking at the pairs of expectant eyes in the audience, Xu Chuan took a deep breath and spoke slowly.

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

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

After a pause, Xu Chuan did not go straight to the point as usual. He changed the subject and continued: "Before officially starting the report meeting, I would like to insert some digressions."

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

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

"Each of them promotes the progress of our civilization and science."

"Just like the mass-energy equation, it can be said to be one of the simplest physical formulas, but it is one of the most profound mysteries in the universe. Through its research, we have revealed the nature of light, found a ruler to measure the universe, and also learned about the conservation of mass and energy."

"Just like through the study of Maxwell's equations, we can use the power grid to quickly and efficiently transmit and use electrical energy; but "In order to efficiently and widely transmit information using radio waves."

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

"It's just that we have not been able to deeply understand the essence of its research."

"Even in the 19th century, we have summarized a set of methods and equations to summarize the laws of fluid motion."

"But to this day, we still know the deeper mathematics, physics and motion implications behind this set of methods and equations. "

"Just like a high-speed flying aircraft, limited by the accuracy and efficiency of the numerical solution of the NS equation, its appearance design still needs to rely on wind tunnels for a lot of experiments, and numerical solutions cannot completely replace wind tunnel experiments so far."

"Why don't passenger planes flying in the sky suddenly disintegrate? Why doesn't the calm earth collapse on its own? What exactly is constraining the diffusion effect of fluids?"

"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 PPT copy that was projected turned a new chapter.

"OK, the digression is over, let's get down to business now."

"I believe that everyone here has read my paper before coming here. I will not repeat the proof in the paper in full."

"In today's report, I will focus on the key nodes in proving the NS equations and the new mathematical tool 'microelement construction method' used."

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

"Let's not talk too much, let's get into the report."

"The incompressible Navier-Stokes equations describe the motion of viscous incompressible homogeneous fluids. According to the conservation of mass and momentum in Newton mechanics, we get the following equations:

【tuνu +(u·)u =p + f，·u =n∑i=1iui = 0】

As Xu Chuan began to formally enter the report, the audience in the audience gathered their energy and stared at the curtain nearest to them, focusing on the reflected pictures and calculations.

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

"Generally speaking, the derivation of the NS equation is based on the force analysis of the fluid microcluster and Newton's law. We can make no assumptions about the fluid, then μ, density, etc., will also have partial derivatives in the three directions. Eq. It would be very complicated.”

【3∑i=1（xi(H(φ)φxi)= 0).】

". If the flow after the shock wave is described by irrotational flow, by introducing the potential function φ, the Euler 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 and explained the key proof steps of the NS equation in a calm and orderly manner while looking at the projection screen.

For solving difficult problems in fluids, 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 that point may change; while the Lagrangian method tracks each fluid particle.

These two methods were one of the most commonly used methods by mathematicians in the past when studying NS equations and fluid mechanics. They did not require him to explain them too much, so Xu Chuan just taught them.

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

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

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

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

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

As Xu Chuan explained, a bright light shone in his eyes, and the trace of doubt that was still there gradually dissipated along with the voice on the podium.

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

After understanding all the key points, Terence Tao leaned on his back gently, with a hint of realization and sigh coming out of his mouth.

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

Hearing this, Terence Tao 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 would have understood it before the report meeting."

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

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

Hearing this, Tao Zhexuan suddenly understood and said with a hint of envy: "So that's it. It seems that you guys have gained a lot from your exchange. 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 over here to communicate in advance, he would have come over to join in no matter what.

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

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 get the consistency of v independent of time, and by proving the consistent boundedness of θ heta θ, we can get the following equation:"

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

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

With Xu Chuan's narration, the 'microelement construction method' was gradually introduced into the proof of the last step of the NS equation.

Regarding the overall existence of the smooth solution of the three-dimensional incompressible Navier-Stokes equation, it is like a space elevator in science fiction novels, going directly from the earth to space. The whole process is extremely clean and neat, without any extra space.

As time passed, the finishing process officially came out of Xu Chuan's mouth.

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

Sitting next to Witten, Roger Penrose poked Edward Witten next to him with his hand, and asked with solemnity and question in his eyes.

"Do you understand?"

To be honest, he didn't understand much of the entire report, maybe less than half?

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 fields such as geometry and abstract structures.

Regarding knowledge in fields such as topology and partial differential equations, although those who study physics basically know something about it, they basically only know a little bit.

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

So he started to feel a little confused when he heard half of it, especially when the "microelement construction method" was introduced.

Edward Witten, who was sitting next to him, replied without turning his head after hearing the question: "It's OK."

His ability in mathematics is not comparable to Penrose. He specializes in quantum field theory, string theory, and related mathematical fields such as topology and geometry.

Although the NS equation is not within his research scope, many of the methods used by his student are topological.

Hearing this, Roger Penrose raised his eyebrows and felt a little heartbroken. He was also a mathematical physicist, but he actually understood it?

After thinking about it, he asked, "Do you regret it?"

Hearing this, Witten, who was listening to the final report, couldn't help but twitch his mouth.

This person is so annoying!

PS: There is another chapter in the evening, please vote for me!