Chapter 422 Existence! Smooth!
Lu Zhou originally thought that he was used to this feeling.
Unexpectedly, when he stood here, it was still difficult to restrain the surging heart.
It was different from the report held in Lecture Hall 1 of the Institute for Advanced Study in Princeton. This time, he faced not only the number theory field, but the entire mathematics field...
Standing on the reporting platform, Lu Zhou took a deep breath to calm down his heart rate.
I looked at the watch for the Nth time.
Looking at the second hand that was getting closer and closer, his face changed into a serious look, and he cheered up.
"It's about to start!"
Nine o'clock sharp.
There is no need for anyone to maintain discipline. When the time reaches the hour, the venue that was originally noisy and chaotic due to the whispered discussions suddenly quiets down.
Under the eyes of everyone, a line of clear titles appeared on the silver-white curtain.
【Proof of Existence and Smoothness of Solutions to the Three-dimensional Incompressible Navier-Stokes Equation】
Responding to the gazes from the audience, Lu Zhou spoke slowly, and started the opening remarks of the report meeting.
"Why doesn't a car traveling at high speed disintegrate itself, why doesn't a still lake explode suddenly?"
"For too long we have been obsessed with the obvious, because the truth we crave has always been disguised as the obvious."
"Even as early as the 19th century, we had already summed up the equation that summarized the law of fluid motion and made it look simple enough, but today, we are still at a loss for the deeper mathematical and physical connotations behind the equation. "
"Mathematics is a rigorous subject. Propositions involving numbers should not be described with ambiguous words like maybe or maybe."
"Returning to the original question, why doesn't a car traveling at high speed disintegrate itself? Why doesn't a still lake suddenly explode? Is there such a mysterious singularity on an infinite time scale that allows our equations to diverge in a finite time ?”
"Now, it's time to answer that question."
The short opening remarks ended, and the PPT on the curtain turned to the next page.
And the report meeting also entered the topic.
In three seconds, Lu Zhou quickly sorted out the thoughts of his speech in his mind. Immediately afterwards, facing the audience, he gave a brief overview of his proof ideas in one minute.
The audience in the audience was silent.
Everyone is staring at the pictures and calculations on the curtain, everyone is listening carefully, unwilling to let go of any detail, unwilling to miss any moment.
[μ(t)=e^(t△)·μ0+∫e^(t-t')△B(μ(t'), μ(t'))dt']
【…】
"When we give a Schwartz divergence-free vector field μ0 to the equation, set the time interval I[0,﹢∞), and then we can continue to define a generalized solution H10 of the Navier-Stokes equation as an integral equation obeying μ(t ), that is, μ→H10df(R3)…”
While the PPT in the curtain was showing, Lu Zhou, holding a laser pointer in his hand, was explaining at the side with an even speech speed.
There is nothing special about the previous part.
Similar things can be seen in many papers on NS equation research.
This part is essential no matter whether the abstract proof method is used to construct the abstract bilinear operator B', or the "L-manifold" method he adopted.
However, the next part is the key to the whole proof idea!
He will introduce the concept of differential manifolds into problems of partial differential equations.
And this is exactly the core of the theory of "using topological methods to study partial differential equations"!
...
Under the stage, Xu Chenyang's face was serious, and the tip of the pen in his hand was lightly tapping on the notebook.
After a while, he whispered to Zhang Wei who was sitting next to him with a voice that only two people could hear.
"Do you understand?"
Zhang Wei shook his head: "I don't do much more research on partial differential equations than you do. If you start to feel strenuous, then I'm about the same."
Zhang Wei's field of expertise is similar to that of his mentor Zhang Shouwu. He mainly focuses on representation theory and the Langlands program, and also studies the Dirichlet L function.
Partial differential equations are not his field of expertise, and he has only learned about NS equations because of his interest.
After all, it is impossible for everyone to be as talented as Terence Tao, who can prove the weak conjecture of Goldbach's conjecture while studying the abstract proof of the NS equation, and even spare time to read Shinichi Mochizuki's paper...
In the world of mathematics, all-rounders are not absent.
But even rarer than giant pandas...
Looking at the formula on the curtain, Xu Chenyang couldn't help feeling: "It's unbelievable..."
Zhang Wei: "What is unbelievable?"
Xu Chenyang: "Number Theory, Abstract Algebra, Functional Analysis, Topology, Differential Geometry, Partial Differential Equations... Is there any direction that he is not good at?"
"Perhaps... algebraic geometry?" Zhang Wei's voice was full of uncertainty when he said this.
Because he just said this sentence, he remembered that Lu Zhou's mentor was Deligne, and the patriarch was also the legendary "father of modern algebraic geometry" and "pope of mathematics" Grothendieck!
The core theories of modern algebraic geometry are basically derived from Grothendieck's few works that have not been lost.
Zhang Wei wouldn't believe it if he said he didn't know algebraic geometry.
At most, it's because I haven't researched that area yet, and the results are still in the making...
...
On stage, the report will continue.
Lu Zhou's speech became faster and faster, and his thinking became clearer and smoother.
The introduction of L-manifold plays a decisive role in the solution of the whole proposition.
It is like a hammer, blasting a gap in the unbreakable maze wall.
With the arrival of this moment, the originally confusing situation instantly became clear.
At the same time, the atmosphere in the venue was also pushed to a climax.
Sitting in the corner of the venue, Fefferman had a smile on his face. From this moment on, he has seen the end.
Tao Zhexuan, who was on the other side of the venue, murmured "I see" in a low voice, with excitement in his eyes.
In the back row of the venue, feeling the heat in the atmosphere, Vera clenched her right hand, and her originally calm heart began to beat faster. In this moment, she is genuinely proud of her mentor...
Also sitting in the back row of the venue, the corners of Faltings' tight mouth suddenly raised an unusual angle.
Noticing the change in the expression on his old friend's face, Deligne asked casually.
"How does it feel?"
Faltings said expressionlessly: "It's so-so."
"Don't you blush when you say that?" Deligne smiled lightly, and returned the gift he had given him before, intact.
The corner of his mouth twitched, Faltings ignored the ridicule of his old friend, glanced at his watch, and stood up slowly.
Deligne: "It's about to end, don't you see the end?"
"That's not necessary."
Anyway, I already understood it all.
Boring questions, or leave it to others to ask.
After leaving this sentence, Professor Faltings did not stop, walked through the crowd sitting on the ground in the aisle, and walked straight to the exit of the venue.
And almost at the moment when Professor Faltings left the lecture hall, the whole report also came to an end.
When the last line of calculation came into view of the audience, there was almost no need for Lu Zhou to make any further explanations.
Because, as the entire audience could see, the final answer was on the horizon.
"...Integrating all the inferences above, it is obvious that the solution to the three-dimensional incompressible Navier-Stokes equation exists, and it is as smooth as we expected!"
That voice, clear and certain.
Not loud, but with a convincing magic.
And the source of that magic power is knowledge.
Almost at the moment when the voice fell.
The audience stood up abruptly from their seats.
The thunderous applause resounded in an instant, and lasted for a long time in this wide and crowded lecture hall...