In the auditorium, there were no seats, and people were buzzing.

Sensational figures and the sounds of head-to-ear discussions converge.

It was not only the scholars in the auditorium who came to participate in the exchange lectures. In the backstage of the auditorium, the teachers and staff of the administrative office of NTU are also busy doing the final inspection.

From microphones to projections, from sound to projections, everything needs to be equipped during the event to ensure that there are no problems.

Although it was not they who came to the stage to give academic presentations.

But honestly, they were more nervous than they were.

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

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

For the academic community, even if it is put on an international scale, such a grand event may not be once in a few years.

On the other side, Xu Chuan sat quietly on a chair in formal clothes and waited for the exchange meeting to begin.

Such scenes were not new to him, and even he was used to them.

Soon, a staff member trotted over and said with a look of adoration: "Professor Xu, it's already 8:55, you see?" ”

Xu Chuan nodded, got up and said, "Thank you." ”

After straightening out his costume and smoothing out his wrinkles, he walked towards the front desk.

Although the report began at 9 o'clock, as the speaker, he took the stage a little earlier to show respect and etiquette to the scholars who came to participate in the report.

When Xu Chuan slowly walked onto the podium, in the auditorium, everyone's eyes were cast.

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

Standing on the podium, Xu Chuan looked down on the audience.

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

[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 of the audience, Xu Chuan took a deep breath and said slowly.

"First of all, I would like to welcome all of you who came to participate in the exchange report, and I am very grateful to all of you for taking time out of your busy schedules to come here to listen to my academic presentation."

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

After a pause, Xu Chuan did not go directly to the topic as before, he changed his words, and continued: "Before officially starting to enter the report meeting, I would like to insert 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 equation, and so on."

"Each of them has contributed to the progress of our civilization and science."

Like the mass-energy equation, it is arguably 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, found the ruler to measure the universe, and also learned the conservation of mass and energy."

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

"And in the NS equation, there is also such an esoteric and hidden meaning."

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

"Even in the nineteenth century, we have already come up with a set of methods and equations to summarize 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."

"Just like a high-speed flying aircraft, limited by the accuracy and efficiency of the numerical solution of the NS equation, we still need to rely on the wind tunnel to carry out a large number of experiments in its shape design, and the numerical solution cannot completely replace the wind tunnel experiment."

"Why didn't the airliner flying in the sky suddenly disintegrate? Why doesn't the calm earth collapse on its own, and what is the diffusion effect of the fluid that is constraining it?"

"All of 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 screened turned over a new chapter.

"OK, the digression is over, now it's officially down to business."

"I'm sure all of you here have read my paper before coming here. As for the proof in the paper, I will not repeat it completely. ”

"In today's presentation, I will focus on the key nodes in proving the NS equation and the new mathematical tool 'micro-element construction method' used."

"I'm sure you're interested in these things, too."

"Without further ado, let's move on to the report."

"The incompressible Navier-Stokes equation describes the motion of a viscous incompressible homogeneous fluid. Based on the conservation of mass and momentum 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 gathered their spirits, staring at the curtain closest to them with full attention, and their eyes fell on the pictures and calculations reflected.

Everyone was listening carefully, unwilling to let go of a single detail, unwilling to miss a single moment.

Generally speaking, the deduction of the NS equation is to analyze the force of the fluid micro-group. If we don't make any assumptions about fluids, then μ, density, etc., will also have partial derivatives in all three directions, and the equations will be very complex."

【3∑i=1（xi(H(φ)φxi)= 0）.】

By describing the flow after the shock wave as a swirl-free flow, the Euler equations can be reduced to a second-order nonlinear partial differential equation called the geopotential flow equation by introducing the φ of the potential function."

“.”

On the podium, Xu Chuan held a 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.

Both Euler and Lagrangian methods are necessary for solving fluid problems.

Euler's method is a description of the velocity and force at each point in Euclidean space, but the fluid particles corresponding to that point may change. Whereas, the Lagrangian method tracks every fluid particle.

These two methods are one of the most commonly used methods by mathematicians in the past to study the NS equation and fluid mechanics, and there is no need for him to focus too much on it, so Xu Chuan also brought it directly.

Next, it is the key point of proving the NS equation process!

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

This was his key tool for proving the NS equation and the central point of introducing the concept of topological geometry into differential and partial differential equations.

In the auditorium, Tao Zhexuan sat beside Deligne and listened carefully to the report.

And when the 'Micro Element Construction Method' appeared, he sat up straight and stared at the screen tightly.

With Xu Chuan's explanation, his eyes also danced with a bright light, and there was still a trace of doubt, which gradually dissipated with the voice on the podium.

"I see, he's such a genius!"

After understanding all the key points, Tao Zhexuan leaned lightly on his back, and spit out of his mouth with a hint 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." ”

Hearing this, Tao Zhexuan looked over with some curiosity and asked, "How do I feel that you have figured out all the looks of this paper before the report meeting?" ”

Deligne smiled and said, "If you also participated in the European mathematics exchange half a month ago, you can also understand it before the presentation." ”

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

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

Hearing this, Tao Zhexuan suddenly understood, and said with a hint of envy: "I see, it seems that the exchange between them has gained a lot, but I missed it." ”

He knew about the exchange 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 over to make up for it no matter what he said.

This kind of academic exchange between so many top mathematicians is really hard to come across.

Especially for someone like him who wants to go further academically.

On the podium, Xu Chuan's report continued.

Using the standard energy calculations we can get the consistency of v, independent of time, and by proving the consistent boundedness of θhetaθ, 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 θ-L∞(0,∞; L p ) norm is bounded, and at the same time, this equation is utilized.

With Xu Chuan's introduction, the 'microstructure method' was gradually introduced into the proof of the last step of the NS equation.

For the problem of the overall existence of a smooth solution of the three-dimensional incompressible Navier-Stokes equation, it is like a space elevator in science fiction, from Earth to space, and the whole process is extremely clean, without a trace of more than a place.

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

In the auditorium, the quiet atmosphere is slowly filled with various emotions such as anticipation, confusion, nervousness, and suddenness.

Sitting next to Witten, Roger Penrose stabbed Edward Witten beside him with his hand, and asked with solemnity and questions in his eyes.

"Do you understand?"

To be honest, the whole report will come down, and he doesn't understand a lot, maybe less than half?

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

Even some achievements in mathematics are limited to the fields of geometry and abstract structures.

For the knowledge of topology, partial differential equations and other fields, although the basic knowledge of physics is understood, it is basically only a little understanding.

It is unlikely that it will be used to study advanced and cutting-edge fields of mathematics.

So when he heard half of it, especially when the 'micro-element construction method' began to be introduced, he began to be a little confused.

And sitting next to him, after hearing the inquiry, Edward Witten replied without replying: "It's okay." ”

His ability in mathematics was not comparable to Penrose's. He specializes in several mathematical areas such as quantum field theory, string theory, and related topology and geometry.

Although the NS equation was not in his field of study, many of the methods he used as a student were topological things.

Hearing this, Roger Penrose raised his eyebrows, feeling a little heartbroken, he is also a mathematical physicist, he actually understood?

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

Hearing this, the corners of Witten's mouth, who was listening to the closing report, twitched involuntarily.

This man is so annoying!

PS: There is one more chapter in the evening, ask for a monthly pass!

(End of chapter)