The top student must be diligent

"Since Professor Xiao has the energy, I believe the recommended students will be very happy."

"Professor Xiao, you have perseverance!"

"Then we won't bother you for now. We have to go back and contact the principal to tell him about the model. When we are sure about it, you can send out this paper."

Looking at the two people's faces trying to hold back their laughter, Xiao Yi always felt that he had agreed a little rashly.

Forget it, why bother about these things.

He said: "Okay, I'll wait for your notification at any time."

Tang Fucheng and Shen Gensheng nodded, and then they were about to leave.

But before leaving, Tang Fucheng said again: "In addition, when you send out this paper, where do you plan to send it? Don't tell me that you want to send only the Chinese version and then send it on your personal website, right?"

Xiao Yi shrugged and said: "I know, don't worry, I will submit it to the Annals of Mathematics at that time."

"That's good, that's good."

Tang Fucheng and Shen Gensheng nodded.

It's not that they don't allow Xiao Yi not to submit to the journal, but for their ultimate plan to call on the international community to jointly develop the explosive trend discrimination model, if the paper is only published on Xiao Yi's personal website, it is obviously not conducive to the dissemination of this matter.

If you want to accomplish this kind of thing, it is still the most important thing to spread it out first.

Then, the two of them left without saying anything more.

Xiao Yi was the only one left in the office again.

He naturally had no objection to publishing the paper in the Annals of Mathematics.

If you want to have an appeal internationally, you still need this kind of top journal to bring influence.

"Okay, the next step is to wait for the results from the school, and then I will submit it to the Annals of Mathematics."

"As for the next..."

Xiao Yi turned the computer screen back and looked at the paper on it.

Since he has found the formation principle of the explosive solution, then he can use this principle to construct a perfect initial condition.

From a mathematical point of view, the proof of existence and smooth solution of NS equations often requires setting an initial condition. Initial conditions are crucial in the study of partial differential equations because they determine the state of the fluid at time t=0, thus affecting the behavior and properties of the solution during the entire time evolution process.

But just as Xiao Yi was about to start thinking along the common thinking inertia of the mathematical community, he suddenly raised his eyebrows.

"In the past, in the study of NS equations, the reason for setting initial conditions was to avoid the influence of similar explosive solutions."

"But now, with the theory of explosive trend, it seems that we can try to prove it from a more general initial condition?"

Thinking of this, Xiao Yi pondered.

If a more general initial condition proof can be achieved, its significance to the entire industry is of course quite high.

First of all, if a specific initial condition is set, the function of this initial condition must be smooth, which is also for the convenience of the subsequent proof.

However, in real conditions, initial conditions are often not so smooth. For example, data in atmospheric and ocean dynamics may be irregular or incomplete. Studying more general initial conditions can enable the NS equations to model these practical problems more accurately.

For some complex flow simulations such as aerospace and automotive industries, the initial conditions may contain irregular boundaries and multi-scale features. More general initial conditions can help improve the accuracy and predictability of these complex flow simulations.

Of course, these are all in terms of application value. Theoretically, more general proofs can also help improve the NS equations, making them more abstract, so as to cover a wider range of initial condition types.

In short, more general proofs are definitely more valuable than proofs under specific conditions.

The latter, in terms of purpose, is more just to solve this problem, rather than for the wider applicability of the final answer.

"But inevitably, this will make the proof more difficult."

Xiao Yi rubbed his head and thought helplessly.

The more general and abstract, the more difficult.

Well, let's think back to why he wanted to prove the NS equation.

For the sake of that plate of vinegar, he made more and more dumplings.

However, he soon put these thoughts aside.

It's just a little harder, challenging, which is exactly what he wants.

"Consider the more generalized initial conditions of the NS equation, among which we can roughly consider a variety of related function spaces."

"Well... first is Lebesgue space."

[Definition: L^p(R^n)={f:R^n→R∣∥f∥L^p=(∫_R^n∣f(x)∣^pdx)^(1/p)\u003c∞}, where 1≤p≤∞]

He simply wrote down the first function space on the draft paper.

Then he immediately began to think about the function space of the second generalized initial condition.

"Sobolev space, well, this space can be used to study functions with a certain smoothness."

[H^s(R^n)={f∈L2(Rn)∣∥f∥H……]

The number of spaces he listed on the draft paper gradually increased, including Besov space, Morrey space, and so on.

If you want to explore more general proofs, it is a very effective method to discuss from different function spaces.

In this way, time passed, and his analysis gradually entered a deeper level.

...

Soon, Tang Fucheng and Shen Gensheng discussed this with President Bao. As they had expected, President Bao was of course very supportive of this matter. They could even see how much influence this would have on improving the status of USTC in the entire industrial field.

After all, fluid mechanics covers every small corner of the industrial field.

In addition to the industrial field, there are other places where fluid mechanics analysis may be used, whether it is atmospheric science or even in games. Maybe future game manufacturers will use this model to simulate sufficiently realistic fluids in games?

This is almost inevitable.

In order to make this matter more widely known, USTC also contacted the government, and some large enterprises with good relationships, whether state-owned enterprises or private enterprises, all participated in this matter.

As everything was ready, Xiao Yi got the news, and then his paper entered the editor-in-chief's mailbox of the Annals of Mathematics through an exclusive channel.

…

In Princeton University, in the editor-in-chief's office of the Annals of Mathematics.

Peter Sanak looked at the new submission in his mailbox, raised his eyebrows slightly, and became interested.

"Xiao Yi's paper?"

It has been a long time since he saw Xiao Yi's pure mathematics paper.

It seems that this mathematical genius, who has been somewhat rebellious in the eyes of everyone in the mathematics community, has now returned to the embrace of pure mathematics.

But after he opened the paper and saw the title, he finally shook his head helplessly.

"Okay, it seems that I thought too much."

"The formation mechanism of PDEs and dynamic system blow-up solutions", judging from such a title, it is definitely not completely in the field of pure mathematics, and it also involves applied mathematics and physics to some extent.

However, Sanak narrowed his eyes again at this time.

"But... his paper claims to have solved the formation principle of blast solution?"

He knew a little about the blast solution problem and was very clear about how difficult it was to solve in related fields.

Unexpectedly, Xiao Yi actually aimed his goal at this problem?

He began to read below.

But soon, he shook his head with a little regret.

This paper was not his cup of tea, he couldn't understand it.

"Well... since it mainly involves the field of partial differential equations, then let's find Terence Tao."

As a man who knows a little about everything, Terence Tao's attainments in the field of partial differential equations are also very high.

So then, Sanak contacted Terence Tao directly.

"Hey, Tao, I have a paper in the field of partial differentials here, and I need you to help review the manuscript."

The voice of Terence Tao came from the phone: "Oh? If Professor Sarak can contact me personally, it seems that I may know the author of this paper?"

Sanak is the editor-in-chief, and the authors of the manuscripts he commissioned are basically acquaintances in the industry.

Compared with other disciplines, the top circle of mathematics is not that big.

Sanak smiled and said, "Of course, this paper is from Xiao Yi."

"Oh?"

Tao's voice immediately showed a little more interest, "OK, send me his paper quickly, I haven't read his mathematics paper for a long time, I hope it can bring me some surprises."

Sanak: "You will not be disappointed."

...

In Tao's office at the University of California, Los Angeles.

As the notification of a new email popped up on the computer, Tao couldn't wait to click on his mailbox and download the attachment.

After opening the paper, the title immediately aroused his great interest.

"The formation principle of the blasting solution?"

His eyebrows widened slightly, feeling quite surprised.