For ordinary people, compared with world-famous mathematical problems such as the Riemann Hypothesis, Fermat's Last Theorem, and Goldbach's Conjecture, the "Navier-Stokes Equation" seems quite unfamiliar. Most people don't even know it.

What the hell is this.

But for Qin Ke, who has been fond of mathematics and science since he was a child, the "Navier-Stokes equation" is a thunderous existence!

The "Navier-Stokes equation", referred to as the N-S equation, is a well-known set of nonlinear partial differential equations in both the mathematics and physics circles. It is called the "Newton of fluid motion" in the industry.

"The Second Law" mainly describes the basic mechanical laws of the flow of viscous incompressible fluids (such as liquids and air).

Since this equation of motion was proposed by Claude-Louis Navier in 1827 based on the theory of fluid momentum conservation, Poisson, Saint-Venant and George Stokes have conducted in-depth research respectively.

It was finally derived in 1945, forming a series of extremely complex equations.

The N-S equation is also known as one of the most useful equations in the world because it establishes the change rate (force) of the particle momentum of the fluid and the change in pressure and dissipation viscous force (similar to friction force) acting inside the liquid.

resulting from molecular interactions) and the relationship between gravity.

It is precisely because it establishes such a relationship that it can describe the dynamic balance of forces in any given area of ​​the liquid. It is the core of fluid flow modeling and has very important significance in fluid mechanics.

Based on this, it can be used to simulate climate change, ocean current direction, and even global weather systems such as El Niño. It can also be used to study the movement of water in water pipes and even fluid movements such as blood circulation.

It can also be applied to designs specifically related to daily life, such as fluid lift research on wings, hydrodynamic design of vehicle shells, flow diffusion analysis of air pollution effects, etc.

When you see this, do you think it has amazing uses?

The problem is that although the N-S equation is of great significance and is very practical, it is a nonlinear partial differential equation, which is very difficult and complicated to solve. Before further development and breakthroughs in solving ideas or technologies, it can only be solved in some very simple special case flow problems.

Only in this way can the exact solution be obtained.

At present, mathematicians around the world have still not been able to prove whether the N-S equation has a smooth solution in three-dimensional coordinates and under specific initial conditions, nor have they proven that if such a solution exists, its kinetic energy has upper and lower bounds.

The above sentence is explained in an easy-to-understand way, that is, the entire world of mathematics is now looking for a general solution to the N-S equation to prove that the solution to this equation always exists, so that any equation can be accurately described through this set of equations.

Fluid, under any starting conditions, at any point in time in the future.

But for a set of equations such as the N-S equations that are difficult to explain using mathematical theory, it is so difficult to prove that the solution to this set of equations always exists!

Therefore, after countless mathematicians have invested countless efforts over the past two hundred years, only about a hundred special solutions have been solved. The only one that can really be regarded as a special achievement was the mathematician Jean Leray in 1934.

It is proved that there is a weak solution to the N-S equation, which can satisfy the N-S equation on the average value, but that is all and cannot be satisfied at every point.

In addition, Master Tao, a mathematician of Xia origin, also wrote a paper "Finite time blowup for an averaged three-dimensional Navier-Stokes equation", which formalized the supercritical state barrier of the global regularity problem of the N-S equation, making the N-S equation

Research has made new progress, but it is still far away from solving the "problems of existence and smoothness of the N-S equation".

For this reason, "the problem of the existence of smooth solutions to N-S equations in three-dimensional space" has been set as one of the seven Millennium Prize problems by the Cray Institute of Mathematics in the United States.

It can be said that whoever can study this problem clearly and find and prove this general solution will catalyze countless new mathematical tools, mathematical methods, and physical theories, leading the mathematical and physical worlds to achieve step-by-step development!

By then, basically the Nobel Prize in Physics, the Marcel Grossmann Prize, the Fields Medal in Mathematics, the Crafford Medal, the Wolf Prize in Mathematics and other major awards will be available, let alone

It is said that it has brought huge social and economic benefits and promoted human civilization!

It is precisely because he is well aware of the difficulty and significance of the Navier-Stokes equation that when Qin Ke saw that the reward given by the system was actually "Exploration and detailed solution of the nonlinear partial differential equation 'Navier-Stokes equation'" (

(Part 1)", there was only one thought in my mind - no matter what, I must get this reward!

Although I don't know whether this "exploration and detailed solution" can prove "the existence of smooth solutions to the N-S equations in three-dimensional space" and find the general solution to the equations, Qin Ke's incredibly rich understanding of this system

With an understanding of the knowledge base, this knowledge rated S-level must be shocking!

As long as he can understand it thoroughly, even if it is just the "first part", it will be enough to make Qin Ke famous in the world of mathematics. By then, not to mention Qingmu, Beiyan University, and Princeton University, which has always been known for its arrogance, will probably come.

I begged him to go to school, oh no, he should be a teacher!

However, Qin Ke quickly calmed down. Even if he gained this knowledge, he still had to be able to understand it!

At least he must have a very solid foundation in college physics, a foundation in college mathematics, and even a higher-level graduate student with doctoral knowledge. Otherwise, if the knowledge is given to him, he will be blind if he can't understand it.

This chapter is not finished yet, please click on the next page to continue reading the exciting content! Even if you understand it in the future, do thorough research, and want to publish it, you must be famous enough and have the aura of a super mathematical genius. In this way, the paper you publish

Only then can it be taken seriously by the mathematical community and not cause suspicion and drag people away for sectioning and dissection.

To this end, Qin Ke must continue his journey in mathematics competitions. IMO gold medals and even championships are indispensable. Physics competitions must also enter world competitions, and professional papers in mathematics must also be started.

.

From this perspective, the system has been guiding him on the right path through tasks.

At least publishing some mathematical papers at an academic level first, and accumulating reputation is a necessary first step.

If there is a chance in the future, I will also start writing academic papers on physics.

Competitions and academic papers complement each other to establish his status and image as a top mathematician and physicist in the future. It will be logical for him to publish a paper on the "Navier-Stokes Equation" by then.

After looking up at the stars and the future, Qin Ke returned his attention to the task itself - publishing his first academic paper, and it had to be a professional academic paper on "mathematical analysis" in a national academic journal.

But academic papers...

I have only written an essay of 800 words, so you want me to write an academic paper?

Qin Ke fell into deep thought, and then decided to ask Professor Shi Cunyuan in the front row for advice. After all, this was a graduate tutor at a prestigious university. Although Yuanzhou University was incomparable to Qingbei, it was also the best university in Huahai Province.

, ranked 985,211.

Shi Cunyuan’s academic level in mathematics is beyond doubt.
Chapter completed!