The four of them stood together and chatted for a while.

Seeing that this group of sign-in people was almost here, the staff of Jiangda who was in charge of reception at the scene took them to the parking lot, got on a bus, and went straight to Jiangcheng.

Schultz and the others had a good chat, and after getting into the car, they sat down in the front and back rows.

"Grigory, what have you been working on for the past few years?"

Shinichi Mochizuki and Perelman sat side by side and asked.

Perelman said with a sigh of relief: "N-S equation! ”

"N-S equation?!"

Whether it was Shinichi Mochizuki or Schultz and Sticks, who were sitting in the front row of them, they were all taken aback.

The problem of the existence and smoothness of the N-S equation is also one of the seven major mathematical problems of the millennium, which is of great significance both mathematically and physically.

Mathematically, the N-S equation is a type of nonlinear partial differential equation, and its smooth solution can allow humans to understand the structure of the equation more deeply and determine whether the nonlinear partial differential equation may have an irregular asymptotic solution for a long time.

In physics, once the existence and smoothness of the N-S equation are proven, human beings can better understand the physical process of turbulence, and then promote the progress of various fields of industry such as aerospace, shipbuilding, and chemical engineering.

Shinichi Mochizuki: "Is there any progress?" ”

Perelman shook his head and said, "It's not much progress, but I feel that the theoretical framework of Ponzi geometry may help me solve this problem, which is why I came here this time." ”

Schultz and the others couldn't help but look at each other.

Then.

Ding Dong –

Scholz's cell phone rang suddenly.

Schultz picked up his phone, slightly stunned.

Faltins sent him a message via WhatsApp.

Because the content of Pang Xuelin's board book was understood in Paris last time, this time, the two bigwigs, Faltins and Deligne, did not come to Jiangcheng.

But the message sent by Faltins was related to Pang Xuelin.

[Schultz, Pang has just published three papers on arXiv, I think the third one, you should focus on it!] 】

At the end of the message, there is a link to the arXiv paper.

Schultz clicked on the link and looked at it for nearly five or six minutes before he looked up and said, "Pang just uploaded three new papers on arXiv. The first is called "Ponzi Geometry" and the second is "A Method of Proof of the ABC Conjecture", but what really matters is the third paper, which is entitled "A Broadly Significant Method for Solving Analytical Solutions of Nonlinear Partial Differential Equations......"

When the words fell, Jacob Sticks, Shinichi Mochizuki, Perelman and others who were sitting near him were all stunned, and their faces showed shock.

A broadly meaningful way to solve systems of nonlinear partial differential equations?

Isn't this what Perelman just said, that the Ponzi framework has the potential to help solve the problem of the existence and smoothness of the N-S equation?

If Pang Xuelin really finds such a method, then the international mathematical community will take a big step forward in proving the existence and smoothness of the N-S equation.

Soon, people began to find out that Pang Xuelin had uploaded a new paper on arXiv, and the car suddenly became noisy.

"Pang has uploaded his paper on arXiv!"

"The paper is finally out, and the content in the board book jumps too much, and it should be much easier to understand with the paper as a reference."

"What about the third paper? A universal way to solve systems of nonlinear partial differential equations, is this a joke? ”

"Is Ponzi geometry still related to systems of nonlinear partial differential equations?"

"If he really found a way to solve the analytical solution of a system of nonlinear partial differential equations in a general sense, wouldn't that mean that the N-S equation could also be proved?"

……

Inside the bus, the mathematicians at the meeting had a lot of discussions.

You must know that a large part of the nonlinear partial differential equations are to describe the operation laws of the world itself and establish corresponding mathematical models.

For example, the aerodynamic model in aircraft design, the absorption and mass transfer dynamics model in chemical engineering, such as the N-S equation that describes the conservation of momentum in viscous incompressible fluids, one of the seven major problems of the millennium......

At present, a variety of methods have been developed to find accurate solutions for different types of nonlinear partial differential equations.

For example, Tanh function method, Sine cosine method, Jacobi elliptic function expansion method, Riccati equation method and F-expansion method.

These methods generally use computer algebra systems to give approximations of nonlinear partial differential equations.

However, the method itself is cumbersome, and the solution given is not necessarily accurate.

And it is only valid for some nonlinear partial differential equations.

If Pang Xuelin really finds a way to solve the analytical solution of the system of nonlinear equations in the general sense, then not only can the process of solving the system of nonlinear partial differential equations be greatly simplified, but also the accuracy of the solution can be greatly improved.

It is self-evident what this means for the entire scientific and engineering community.

Of course, even if Pang Xuelin gives a method for finding analytical solutions to nonlinear partial differential equations, it does not mean that all nonlinear partial differentials can be solved exactly.

After all, the world itself is chaotic, and the complexity of the partial differential equation itself is a reflection of the complexity of the world itself.

If nothing else, take the heat equation and the wave equation as examples.

There are so-called regular solutions in the thermal equation, which improve the properties of the solution.

This means that given a continuous but insignificant initial value condition, take it to the heat equation, and in an instant, it will become smooth at any time t greater than 0.

But that's not a good thing.

This also means that the inverted heat equation deteriorates the properties of the solution.

Therefore, for the inverted heat equation, there must be a smooth (infinitely differentiable) initial value condition to ensure the existence of the solution.

Let's talk about the wave equation.

The wave equation does not have a regular solution, and given a quadratically differentiable initial value condition to the wave equation, it does not return a cubic differentiable solution.

The same is true for the N-S equation.

……

After a while, the bus quieted down.

Most people either hold their mobile phones or find their notebooks and start downloading and flipping through Pang Xuelin's papers.

Everyone understands that if Pang Xuelin really solves the problem of the analytical solution of nonlinear partial differential equations, then this time, the influence of his work will go far beyond the mathematical community.

……

Jiangcheng University, Faculty Apartment.

Pang Xuelin stretched, he has been writing papers in the past three weeks.

Finally, before the presentation, all the papers on Ponzi geometry, ABC conjecture proof, and analytical solutions of nonlinear partial differential equations were uploaded to arXiv.

After arXiv took over, he submitted these three papers to the Annals of Mathematics.

This is what he had promised to Deligne before leaving Paris.

The last time he was in Paris, he didn't publish the analytical solution to a system of nonlinear partial differential equations using Ponzi geometry because of lack of time.

This time, he is going to announce all the achievements he has made in the Martian World and the Wandering Earth World.

After doing these things, Pang Xuelin breathed a long sigh of relief.

Then, he got up and went to the kitchen, took a jug of milk from the refrigerator and drank it in one gulp.

Then, Pang Xuelin left another word for Qi Xin, then muted the phone, returned to bed, and fell asleep directly.

Tomorrow is the day of the opening of the presentation, and he must be ready to be questioned by mathematicians from all over the world.