The Science Fiction World of Xueba

The four stood together and chatted for a while.

Seeing that the group of sign-in people had almost arrived, the Jiang University staff who were in charge of reception took them to the parking lot, boarded a bus, and headed straight to Jiangcheng.

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

"Grigory, what subject have you been researching these past few years?"

Mochizuki Shinichi and Perelman sat side by side and asked.

Perelman sighed, "N-S equation!"

"N-S equation?!"

No matter it was Mochizuki Shinichi, or Schultz and Sticks sitting in the front row of them, they were all taken aback.

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

Mathematically, the N-S equation is a kind of nonlinear partial differential equation. 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 a long-term irregular asymptotic solution.

In physics, once the existence and smoothness of N-S equations are proved, human beings can have a deeper understanding of the physical process of turbulence, and then promote the progress of various industries such as aerospace, shipbuilding, and chemical engineering.

Mochizuki said, "Is there any progress?"

Perelman shook his head and said, "Not much progress has been made, but I feel that the theoretical framework of Ponzi geometry may be able to help me solve this problem, which is why I came here this time."

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

At this time.

Ding dong——

Schultz's cell phone rang suddenly.

Schultz picked up the phone and was slightly taken aback.

Faltings sent him a message via WhatsApp.

Because the content of Pang Xuelin's writing on the blackboard was well understood last time in Paris, therefore, this time, the two big men, Faltings and Deligne, did not come to Jiangcheng.

But the information sent by Faltings is related to Pang Xuelin.

[Schultz, Pang just released three papers on arXiv, and I think you should pay more attention to the third paper! 】

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

Schultz clicked on the link, watched it for about five or six minutes, and then raised his head and said: "Pang just uploaded three new papers on arXiv. The first one is called "Ponzi Geometry", and the second one is "One of the abc conjectures." A Method of Proof", but the really important one is the third paper, which is entitled "A Method of General Significance for Analytical Solutions of Nonlinear Partial Differential Equations..."

After the words fell, Jacob Stix, Mochizuki Shinichi, Perelman and others sitting near him were stunned, with shocked expressions on their faces.

A method of general significance for solving systems of nonlinear partial differential equations?

Isn't this just what Perelman said just now, is it possible that the theoretical framework of Ponzi geometry can help solve the problems of the existence and smoothness of N-S equations?

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 in the bus began to discover that Pang Xuelin had uploaded new papers on arXiv, and the bus suddenly became noisy.

"Pang uploaded the paper on arXiv!"

"The thesis has finally come out. The content in the blackboard is too jumpy. With the thesis as a reference, it should be much easier to understand."

"What about the third paper? A general method for solving systems of nonlinear partial differential equations. Are you kidding me?"

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

"If he really finds a way to solve the analytical solutions of nonlinear partial differential equations in a general sense,

Doesn't that mean that the N-S equation may also be proved? "

...

Inside the bus, the mathematicians attending the meeting were discussing one after another.

It should be known that a large part of nonlinear partial differential equations is to describe the operation laws of the world itself and establish corresponding mathematical models.

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

At present, the mathematical community has developed a variety of methods for exact solutions to different types of nonlinear partial differential equations.

Such as Tanh-function method, Sine-Cosine method, elliptic function expansion method, equation method and F-expansion method, etc.

These methods generally rely on computer algebra systems to give approximate values ​​of nonlinear partial differential equations.

But the method itself is more 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 solutions of nonlinear equations in a general sense, then not only can the solution process of nonlinear partial differential equations be greatly simplified, but the accuracy of the solutions can also be greatly improved.

What this means to the entire scientific and engineering community is self-evident.

Of course, even if Pang Xuelin gave a method for finding analytical solutions of nonlinear partial differential equations, it does not mean that all nonlinear partial differential equations can be solved accurately.

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.

Among other things, take the heat equation and the wave equation as examples.

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

This means that as long as a continuous but non-differentiable initial value condition is given and the heat equation is run, it will become smooth at any time t greater than 0 in an instant.

But that's not a good thing.

Because it also means that inverting the heat equation will deteriorate the properties of the solution.

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

Now for the wave equation.

The wave equation does not have a canonical solution, giving the wave equation a quadratically differentiable initial value condition, it will not return a cubicly differentiable solution.

The same is true for N-S equations.

...

After the bus was noisy for a while, it gradually quieted down.

Most people either took their mobile phones or took out their notebooks and started to download and read 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 achievement will go far beyond the world of mathematics.

...

River City University, teachers apartment.

Pang Xuelin stretched his waist. For the past three weeks, he has been writing a thesis in a hurry.

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

After arXiv occupied the pit, he submitted these three papers to the Annals of Mathematics.

This was something he had promised Deligne before leaving Paris.

When he was in Paris last time, due to lack of time, he did not publish the content of the analytical solution of nonlinear partial differential equations solved by Ponzi geometry.

This time, he plans to announce all the achievements he has made in the Martian world and the world of Wandering Earth.

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

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

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

Tomorrow is the opening day of the symposium, and he must recharge his energy to accept questions from mathematicians all over the world.