MTL - The Science Fiction World of Xueba-Chapter 490 Existence and smoothness of NS equation

"Mr. Schultz, I heard that you are working on the NP problem. Is there any progress now?"

Mochizuki held coffee and looked at Schultz.

Because of the problem of proof of ABC's conjecture, Schultz went to Japan to discuss with Mochizuki, but no one could convince each other.

Although Pang Xuelin later proved the ABC conjecture, Mochizuki Shinichi finally admitted his mistake.

But the relationship between him and Schultz has not been very good.

Therefore, Mochizuki Shinichi asked what he said, and the other few people stopped talking and turned their attention to Schultz, for fear that they would quarrel again.

However, Schultz ’s reaction was a little bland, and he shook his head with a smile: "I do n’t have any clue yet. I still focus on how to combine Ponzi geometry with arithmetic geometry. I always feel that these two There is a connection between theorists' theory. If the research is thorough, it may produce some wonderful chemical reactions. As for the NP-complete problem, I have considered this proposition as a lifetime project to study. "

"The connection between arithmetic geometry and Ponzi geometry?"

Everyone could not help but look at each other.

In the field of arithmetic geometry, Schultz can be regarded as a grandmaster of the Kaishan School. Even Pang Xuelin dare not say whether the research in this field has reached the level of Peter Schultz.

Therefore, everyone seemed a little surprised at the same time that Schultz tried to study the relationship between arithmetic geometry and Ponzi geometry.

If it were not for an idea in this regard, Peter Schultz would not have left Germany to study in a strange environment like Jiang University.

You know, this guy even rejected Princeton's invitation straight away.

But for the complete problem of NP, everyone did not feel much surprised by Peter Schultz's position.

Liu Tingbo, who was on the side, said with a smile: "I don't think the NP problem is directly proven to be good. Otherwise, if you do cryptography research like me, you will lose your job."

When Liu Tingbo said this, everyone suddenly laughed.

Liu Tingbo is right in saying this. If NP = P, it basically means that for any practical encryption system, there is a positive integer k, and an algorithm with a running time of O (X ^ k) can break it.

Seriously speaking, the currency systems of countries around the world based on modern encryption systems will completely collapse, not to mention Bitcoin and the like.

Moreover, this proposition not only affects cryptography, but also has a huge impact on the theory of complex systems.

Including artificial intelligence, condensed matter, life sciences and other systems, these are closely related to human life.

However, current methods of dealing with complex systems rely heavily on numerical calculations. Most problems are difficult to find analytical solutions, and it is naturally impossible to make effective predictions.

Once P = NP is proved, the merchant can find the shortest route, the factory can achieve maximum productivity, and the flight can be properly arranged to avoid delays ...

In a nutshell, any problem can be optimally solved in the shortest time, humans can make better use of available resources, more powerful tools and methods will appear in the scientific, economic and engineering circles, and major breakthroughs will become With the continuous flow, the Nobel Prize selection committee will be too busy to deal with.

Of course, this is an ideal world, including Pang Xuelin, most mathematicians believe that the greatest possibility is P ≠ NP.

But no matter whether the result is true or not, it is very difficult for mathematicians to prove that P = NP or P ≠ NP.

At this time, Schultz said: "Professor Pang, are you sure about the next research direction?"

More than two months ago, Pang Xuelin and Perelman collaborated to complete the proof of Hodge ’s conjecture, and gave a related report at the International Conference of Mathematicians.

Pang Xuelin even raised Pang's fifteen questions, which pointed out the direction for the development of mathematics in the next few decades.

Therefore, everyone is very interested in Pang Xuelin's next research direction.

Pang Xuelin smiled and said, "The existence and smoothness of the NS equation!"

"Not Riemann's conjecture?"

Tao Zhexuan, Perelman and others looked at each other and felt a little surprised.

Pang Xuelin has completed the proof of BSD conjecture, Hodge conjecture, ABC conjecture, twin prime conjecture, and Polignac conjecture. The last three conjectures are basically closely related to the distribution of prime numbers.

Therefore, Pang Xuelin's next research on Riemann's conjecture should be considered a matter of course.

They did not expect how Pang Xuelin suddenly became interested in the existence and smoothness of the NS equation.

Pang Xuelin smiled without explaining.

The reason for choosing the existence and smoothness of the NS equation as the next research direction is more because it is necessary to accurately calculate the plasma turbulence problem in nuclear fusion reactors.

If this proposition is solved, then the design of nuclear fusion reactor control software will become very simple.

The NS equation is very complicated, which involves the coupling of velocity and pressure, the first-order partial derivative, the second-order partial derivative, nonlinear terms and so on.

People's current understanding of the NS equation is still not enough.

For such a complex NS equation, it is not clear whether there is a solution, and it is even more unknown whether the solution is continuous.

In a sense, the NS equation is to fluids just like Newton's second law is to classical mechanics.

Many people may say that it doesn't matter that the equations will not be solved. We have a computer, which can give numerical solutions through numerical simulation plus the method of solving nonlinear equations given by Pang Xuelin.

But the numerical solution will involve the balance between accuracy and computing power. You have to calculate it accurately. It takes a long time for the computer to draw a three-dimensional grid, the inverse relationship of the cube of the grid number and grid size, The number of nodes is roughly the same. Your number of algebraic equations has skyrocketed. A problem can even take decades.

So ~ www.novelbuddy.com ~ Pang Xuelin must solve the problem from the source.

Considering the nature of the solution of the NS equation, on the one hand, the solution must exist, because if it does not exist, then the fluid phenomenon in our life should not exist, or the NS equation itself cannot describe the fluid well.

The second possibility can be ruled out. The problem is to strictly prove its existence. This is a bit like the Jordan theorem. We can probably all be judged by individuals, but there is a big problem if we prove it. Too.

The first step is to prove the existence of the understanding and then look at how large the solution space is, whether you can engage in analytical solutions or asymptotic solutions.

The long-term behavior of the solution is smooth, and even study the topology of the solution space, or define the equation on the solution space and then study the solution space of the equation on the solution space and its topological differential properties.

The existence and smoothness of the NS equation is to study these problems.

If fully understood, human understanding of fluid mechanics will make a tremendous progress.

txt download address:

phone-reading: