In the auditorium, there were no seats and a lot of people.
Sensational figures and whispering discussions gathered together.
The excitement in the auditorium was not limited to the scholars who came to participate in the exchange report. In the backstage of the auditorium, teachers and staff from the Administrative Affairs Office of NTU were also busy doing final inspections.
From microphones to projections, from speakers to projections, all equipment during the exchange meeting must be ensured without any problems.
Although they are not on stage giving academic reports.
But to be honest, they were more nervous than that one.
After all, this is the world's top academic exchange meeting, with more than 3,000 scholars present.
And there are many top mathematicians and top physicists inside.
For academia, even internationally, such a grand event may not happen once every few years.
On the other side, Xu Chuan was wearing a formal suit and sitting quietly on a chair, waiting for the exchange meeting to begin.
For him, such a scene is not unfamiliar, and he is even used to it.
Soon, a staff member ran over and said with admiration: "Professor Xu, the time is already 8:55, do you think it is?"
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 report meeting started at nine o'clock, as the speaker, he took the stage a little earlier as a sign of respect and etiquette for the scholars who came to participate in the report meeting.
When Xu Chuan slowly walked onto the podium, everyone in the auditorium turned their attention to 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, fell silent 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 clear line of titles appeared on the silver-white curtain.
[Proof of the existence and smoothness of solutions to 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 printed Chinese characters.
Looking at the expectant eyes in the audience, Xu Chuan took a deep breath and spoke slowly.
"First of all, welcome to everyone who has come to participate in the exchange report. I am also very grateful to 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 about the proof of the existence and smoothness of the solution to the NS equation."
After a pause, Xu Chuan did not go directly to the topic as before. He changed the topic and continued: "Before officially entering the report meeting, I would like to make some digressions."
"Of course, it's also related to the NS equation."
"In the past, we have gained 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 promotes the progress of our civilization and science."
"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 studying it, we have revealed the nature of light and found the 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 power 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 our research on it has not been able to understand the essence in depth."
"Even in the 19th century, we had already summarized a set of methods and equations to summarize the laws of fluid motion."
"But to this day, we still have only a superficial understanding of the deeper mathematical, physical and motion implications behind this method and equations."
"Just like a high-speed flying aircraft, limited by the accuracy and efficiency of numerical solutions to NS equations, we still need to rely on wind tunnels to conduct a large number of experiments for its shape design. Numerical solutions cannot completely replace wind tunnel experiments so far."
"Why doesn't the passenger plane flying in the sky suddenly disintegrate? Why doesn't the calm earth collapse on its own? What is the constraint of the diffusion effect of fluid?"
"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 displayed turned to a new chapter.
"OK, the digression is over, and now we officially get to the point."
"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 proving the key nodes of the NS equation and the new mathematical tool 'microelement construction method' used."
"I also believe that these are the things that you are interested in."
"Without further ado, let's get into the report."
"The incompressible Navier-Stokes equation describes the motion of a viscous incompressible homogeneous fluid. According to 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 formally enter the report, the audience in the audience gathered their energy and stared at the curtain nearest to them with all their attention, their eyes falling on the reflected pictures and calculations.
Everyone was listening carefully, unwilling to let go of any detail or miss any moment.
"Generally speaking, the overturning of the NS equation is to perform a force analysis on the fluid microcluster and introduce Newton's law. We can not make any assumptions about the fluid, then μ, density, etc. will also have partial derivatives in the three directions. Eq.
It would be very complicated.”
This chapter is not finished yet, please click on the next page to continue reading the exciting content! [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 in detail, 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 the 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 gently leaned on his back, and a sound of sudden realization and sigh came 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 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 come across.
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 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 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 smooth solutions to the three-dimensional incompressible Navier-Stokes equation, it is like the space elevator in science fiction, which goes 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, nervousness, 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 a lot of the whole 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 about it.
It is basically impossible to use it to study advanced and cutting-edge mathematical fields.
So when he heard about it halfway, especially when the 'micro-element construction method' started to be introduced, he started to feel a little confused.
Sitting next to him, after hearing the inquiry, Edward Witten replied without looking back: "It's okay."
His mathematical ability is not comparable to that of Penrose. He specializes in quantum field theory, string theory and related topology and geometry and other mathematical fields.
Although NS equations are not within the scope of his research, many of the methods used by his student are topological.
Hearing this, Roger Penrose raised his eyebrows and felt a little worried. He is also a mathematical physicist, but he actually understood it?
After thinking for a while, he asked: "Then do you regret it?"
Hearing this, Witten, who was listening to the closing report, couldn't help but twitch the corners of his mouth.
This person is so annoying!
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