Ultimate Scholar

Chapter 260 Complete the proof, it belongs to Li Mu's blow-up time!

The same lecture hall was crowded with people.

And outside the gate, there are still a large number of people rushing in.

Obviously, everyone can feel that there are more people attending the report today than in the previous opening ceremonies.

Even, all the seats were filled, so that the back and the aisles on both sides were full of people.

Including the media from various places, there are far more than before.

There were very few media that came to record reports before, basically they were relatively large and official media, but now the media that come here are all kinds of media, not only from Russia, but also from other countries.

Naturally, CCTV reporters from China also appeared here.

CCTV reporter in Russia, Cao Yang looked at the flow of people around and couldn't help sighing: "There are so many people."

On the side, his colleague, Chen Xiaoming, who is also a reporter stationed in Russia like him, nodded and said: "Yes, I have been here several times before, and I have never seen the seats here be full."

He looked around the entire venue, and said with emotion: "This place is full of high-level intellectuals, all of them are math bosses."

"This is the International Congress of Mathematicians, and of course all mathematicians are here."

Later, Tu Chengyu, the head of the Russian correspondent station, said, "Chen Xiaoming, I remember you had a bachelor's degree in mathematics when you were in college."

Chen Xiaoming suddenly felt embarrassed: "Damn, Mr. Tu, don't mention this kind of thing. I haven't studied mathematics for many years."

"At the beginning, I felt that I had some talent in mathematics. After all, I got full marks in mathematics in the college entrance examination, but after four years of studying, forget it, I should give up as soon as possible. Afterwards, I went to Russia to study abroad, so I changed to studying in Russia. finance."

Hearing Chen Xiaoming's words, the other two couldn't help being curious: "Then how did you become a reporter?"

"Isn't it because I learned Russian while studying in Russia?" Chen Xiaoming shrugged. "As for finance in Russia... I can only talk about it, and it's only theoretical."

Tu Chengyu and Cao Yang looked at each other, and couldn't help laughing at the end. Indeed, finance is at most useful in places with relatively developed economies, and the premise is that there are enough connections in the family or assets.

Otherwise, you know everything you know.

Chen Xiaoming immediately became emotional: "So, the majors studied in college often have nothing to do with the final job."

"I really envy someone like Li Mu."

Both Cao Yang and Tu Chengyu nodded in agreement, expressing their approval.

People who can show their talents in college majors are indeed enviable.

The three of them were chatting, and at this moment, a Russian reporter suddenly asked them, "Are you reporters from China?"

The three turned their heads to look, and then nodded: "Yeah, what's the matter?"

The Russian reporter gave them a thumbs up and said, "A truly great mathematician has emerged in your country."

"There used to be quite a few in our country, especially in the last century, but now, there are fewer and fewer."

The three reporters were taken aback by the sudden praise, and of course, they all smiled afterwards.

"Thank you for your compliment, but no matter what, your country's mathematics is still very strong. At least, you still have great mathematicians like Gregory Perelman."

"Perelman..." The Russian reporter shook his head helplessly when he heard this name: "Although he is indeed our pride, but the current him..."

Suddenly, the Russian reporter widened his eyes and looked towards the entrance of the venue: "Wait...is that Perelman?"

The three of Cao Yang were taken aback for a moment, followed his gaze, and immediately found a bearded man walking in from the entrance.

And as long as they are in the world of mathematics, almost no one will be unfamiliar with this bushy and somewhat scruffy beard.

This is the prover of the Poincaré conjecture, Gregory Perelman!

For a while, the entire venue became noisy because of Perelman's entry.

Of course, although people are talking about these mathematicians who have claimed to have left the mathematics world, no one has taken the initiative to talk to him. After all, everyone can basically guess that Perelman probably does not want to talk to anyone. People have too much communication.

Therefore, people were just amazed that Li Mu's report could actually attract him.

In this way, the arrival of Perelman brought the atmosphere of this report to a peak again.

"That is to say, no matter how much Perelman breaks away from the world of mathematics, he cannot remain indifferent to the proof of such an important conjecture."

Wiles, who was sitting in the front row, shook his head and said.

Seeing Perelman stand alone in the last corner, he then sighed with emotion: "It's just, why is this so?"

He should have sat in the same position as them, not alone in the back.

Regarding this, Faltings just said blankly: "It's all a personal choice. We don't need to comment too much. If he is willing to come, it means that he is still sincere about mathematics, which is enough."

Wiles nodded with a smile: "That's true."

"Then look forward to what kind of surprises Li Mu can bring us next."

They all looked at the stage.

The PPT on the big screen has been opened.

Above, it shows the theme of this report.

【Proof: Existence and smoothness of solutions to the Navier-Stokes equation】

And what is listed below this topic is the general form of the Navier-Stokes equation.

Today, this mathematical problem that has been circulated for many, many years in the world of mathematics and physics, will it be terminated from now on?

...

The time came to half past nine.

According to the time plan, this time is exactly the time when the report starts.

Footsteps sounded from the background.

And the figure that appeared was Li Mu.

There is no host to come on stage to control the field first.

However, even if no one was controlling the field, the originally noisy sound of the audience immediately quieted down as Li Mu appeared on the stage.

More than four thousand, nearly five thousand pairs of eyes looked at him closely.

It is he who will prove the problem of the century today.

"Hi everyone, I'm Li Mu."

Seeing so many people in the audience, compared to his second report a few days ago, there were even more people.

He smiled and said: "First of all, I would like to thank the International Congress of Mathematicians and the International Mathematical Union for extending the time for me by one day, so that my third report can still appear in the conference."

"Of course, I am also very grateful to everyone who is willing to work hard and change the itinerary to participate in my report."

"So, I will not disappoint everyone's expectations, and repay everyone with the revelation of the truth."

Immediately, he turned around and walked in front of the big screen.

"Then stop talking nonsense, let's make this report and start officially."

"As I predicted before, in this report, I will prove the existence and smoothness of the solution to the Navier-Stokes equation."

PPT a little bit, enter the next page.

And the ppt content on this page is like an outline, showing in detail the complete steps of his proof process.

This may be a little incomprehensible to those ordinary scholars, but for those real big cows, it has the effect of enlightenment.

The big cows can directly deduce the derivation process of the whole paper through the abstract of a paper, and it is natural for this kind of thing.

"Use the integral space after partial differentiation to constrain the particles of the fluid in space, and then deal with the fluid viscosity coefficient of the Navier-Stokes equation to deal with the time explosion problem..."

Tao Zhexuan spoke in a daze.

Until finally, he reacted suddenly.

"Wait...he just solved the problem of the explosion time!"

Explosion time, of course, does not mean that time has exploded, but it means that in the process of trying to prove the existence and smoothness of the solution of the NS equation, there will often be an increase in the time item, which will lead to the original regular fluid, Suddenly at some point it exploded.

The simplest description is that without the influence of external forces, such as the huge impact brought by the sudden fall of a meteor, the originally calm sea suddenly exploded.

Just like all the particles in seawater, at a certain moment, the internal force will suddenly no longer be chaotic and uniform everywhere, but suddenly have an orderly direction, so the uniform force everywhere becomes The sudden huge pressure caused the fluid to explode.

This is also known as blow-up time in this profession.

This problem has always existed in the research of the NS equation, which has caused headaches for all researchers. Like a paper published by Terence Tao, it was precisely to study this problem, but he also did not solve it well. question.

But now, there is no doubt that Li Mu has solved it.

In fact, Tao Zhexuan and the others understood after reading the outline he listed.

"Yeah... the integrated space is really a perfect one, which can perfectly eliminate internal pressure and balance the various interaction forces between particles."

Deligne also nodded deeply.

"Should have realized it long ago."

...

These big cows couldn't help applauding Li Mu's step in their hearts.

And Li Mu on the stage can roughly guess what the audience is thinking.

When this biggest problem is solved, the following problems will also become very convenient.

However, what was the process before this?

"Integrating space can completely integrate an entire area of ​​fluid, and at the same time, we should never forget the method of differentiation."

"We can also divide this entire area into countless small areas, and then integrate these small areas, which is also the idea embodied in the Boltzmann equation."

"Then, next, we start substituting the general form of the Navier-Stokes equations, and start using the method I just mentioned-I like to call it global differentiation..."

Li Mu came to the blackboard and began to write the following steps on it.

Everyone in the audience focused on what he wrote, and they were also interested in what he just said, dividing the entire area into countless small areas, and then analyzing the overall space.

They can hear that this is obviously a method of using the overall space.

This is exactly what they hope to learn.

However, after Li Mu started to write, everyone was amazed.

This overall differential method, in terms of technical difficulty, is a bit too elegant.

In terms of Go, it is a master hand, in terms of piano music, it is Rachmaninoff's Third Piano Concerto, and the violin music is Paganini's 24th Caprice.

Such skill difficulty...

They had to marvel that Li Mu was still that Li Mu!

Just like the other conjectures he once proved.

Of course, the momentary amazement did not affect their continued thinking following Li Mu's steps.

After completing this part, everything below seems to become clearer.

When the general form of the NS equations is described in the global space, the irregularity of the turbulent flow seems to be obvious.

What the NS equation tries to describe is turbulent flow. Rapid rivers, billowing storm clouds, or smoke from chimneys, etc., all belong to turbulent flow, which is also a problem that fascinates various scholars.

For example, Werner Heisenberg, the famous physicist who proposed Heisenberg’s uncertainty principle, was once asked what question he would most like to ask God if he went to heaven after death, and he replied: "When I meet God, I ask him two questions: Why relativity? Why turbulence? I believe he will only answer the first question."

That is to say, God probably cannot answer the second question.

So, can Li Mu take this issue a step further?

...

The blackboard was gradually filled with writing.

It was full of formulas like heavenly scriptures, making many listeners in the audience a little drowsy for a while.

Those who participated in Li Mu's first report and were surprised that they could understand his report could only smile wryly at this moment, knowing that they were still too young.

It wasn't that they understood Li Mu's report, but Li Mu made them understand the report.

In this way, about forty minutes passed.

According to the previous normal one-hour report, the report is almost over in more than 40 minutes, but obviously everyone present knows that the current report has just passed half, maybe not yet——

When Li Mu finished the finishing touch on the blackboard, he turned around and said, "So here, I have completely controlled every part of the fluid within the integrated space."

"Here we process the timeline, and we can find that no matter how the timeline changes, the blow-up time will no longer appear."

"That is to say, in the past, the explosion time problem we faced was completely solved."

"So--"

As Li Mu's voice fell, the PPT page moved again, and a statement appeared on it.

For this statement, people in the mathematical community are very familiar with it.

[In three-dimensional space and time, given an initial velocity field, there is a vector velocity field and a scalar pressure field, which is the solution of the Navier-Stokes equation, where the velocity field and the pressure field need to satisfy Smooth and globally defined properties. 】

"This statement, I think everyone knows, is the Clay Institute's complete statement of the existence and smoothness of solutions to the Navier-Stokes equations among the seven millennium problems."

"Then, return to Equation 3.3."

Li Mu pointed to the blackboard, and he talked about the combined form of NS equation and integrated space.

"From here on, I will prove the existence of this velocity field and pressure field."

"Of course—" Li Mu smiled slightly: "I think everyone can see the next step."

Ninety-nine percent of everyone: "?"

They saw a ghost!

They haven't seen anything since about tens of minutes ago. \b

In the end, they could only acquiesce that the people Li Mu mentioned were actually the "math masters" sitting in the front rows.

Of course, the bosses in the first few rows were indeed relieved at this time.

The next steps are indeed obvious.

"Under the holistic space, the NS equations become so simple."

"That is to say, the second-order derivative term cannot be avoided, and an exact solution cannot be obtained."

"What are you thinking... It's enough to prove the existence of the solution. For such things as precise solutions, let's ask God after we die."

"Whether God knows or not is hard to say."

Deligne and the others shook their heads and sighed.

It was indeed as they thought, Li Mu didn't even give much explanation for the next steps, and just started writing without any hindrance.

There may still be some problems that ordinary people cannot understand, but for Li Mu, these problems are not really problems.

Until the blackboard was erased and filled with writing again——

"...It has been verified that the velocity field and pressure field are smooth."

"So, I think the final result has come out. Under the three-dimensional space and time, there is indeed a smooth and globally defined vector velocity field and scalar pressure field, which is the Navier-Stokes Solution of the equation."

Having said that, Li Mu also put down the pen in his hand and walked to the front of the podium.

"The undulating waves follow our boat as we meander across the lake, and the turbulent air follows the flight of our modern jet."

"Both mathematicians and physicists are convinced that both breezes and turbulence can be explained and predicted by understanding the solutions to the Navier-Stokes equations."

"And until now."

"If my proof process is rigorous enough, and there are no contradictions and errors that may exist before and after the theory."

"Then I think we can now be sure that there is indeed a smooth solution to the Navier-Stokes equation."

"At this point, we are one step closer to understanding turbulence."

"Some say God probably doesn't know why there is turbulence either."

"But I think we mathematicians and physicists will know eventually!"

Lean your upper body forward slightly.

Then the applause exploded. \b

The blow-up time of the NS equation is over, but the blow-up time belonging to Li Mu has started again!