I really just want to be a scholar

Chapter 182 The Navier-Stokes Equations
For ordinary people, compared with world-renowned mathematical problems such as Riemann's conjecture, Fermat's last theorem, and Goldbach's conjecture, the "Navier-Stokes equation" is quite unfamiliar, and most people don't even know it. What the hell is it.

But for Qin Ke, who liked mathematics and science since he was a child, the "Navier-Stokes equation" is like a thunderbolt!

"Navier-Stokes equation", namely (Navier-Stokes equation), referred to as NS equation, is a well-known nonlinear partial differential equation system in both mathematics and physics. It is called "Newton of fluid motion" by the industry. The Second Law" mainly describes the basic mechanical laws of the flow of viscous incompressible fluids (such as liquids and air, etc.).

Since this equation of motion was proposed by Claude-Louis Navier in 1827 based on the theory of fluid momentum conservation, Poisson, St. Venant and George Stokes have conducted in-depth research respectively. And finally deduced in 1945, forming a series of extremely complex equations.

The NS equation is also known as one of the most useful equations in the world, because it establishes the rate of change (force) of the particle momentum of the fluid and the change of pressure acting on the interior of the liquid and the dissipative viscous force (similar to friction, force, arising from molecular interactions) and the correlation between gravitational forces.

It is precisely because it establishes such a relationship that it can describe the dynamic balance of forces in any given region 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 movement, and even simulate a global meteorological system such as El Niño, and it can also be used to study fluid movement such as water flow in water pipes and even blood circulation.

It can also be applied to specific designs related to daily life, such as the study of fluid lift of airfoils, the hydrodynamic design of vehicle skins, the flow diffusion analysis of air pollution effects, etc.

Seeing this, do you think its uses are amazing?
The problem is that although the NS 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 the solution idea or technology is further developed and broken through, it can only be solved in some very simple special cases of flow problems. to find its exact solution.

At present, mathematicians all over the world are still unable to prove whether the NS equation has a smooth solution under three-dimensional coordinates and specific initial conditions, nor has it been proved that if such a solution exists, its kinetic energy has its upper and lower bounds.

The above sentence is explained in an easy-to-understand way, that is, the mathematical community of the whole world is now looking for the general solution of the NS equation to prove that the solution of the equation always exists, so that any equation can be accurately described by this set of equations. Fluid, at any initial condition, at any point in the future.

However, for a group of equations such as the NS equation, which is difficult to explain by mathematical theory, it is extremely difficult to prove that the solution of this equation system always exists!

So after 200 years, countless mathematicians have invested countless efforts, but only about more than 100 special solutions have been solved. The only one that can be regarded as a special achievement is the mathematician Jean Lerey in 1934. It is proved that the weak solution of the NS equation exists, which can satisfy the NS equation on the average, but it is nothing more than that, and cannot be satisfied at every point.

In addition, Tao Zongshi, a Xia-born mathematician, 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 NS equation, allowing the NS equation to The research has made new progress, but it is still far away from solving the "existence and smoothness of NS equations".

For this reason, "The Existence of Smooth Solutions of NS Equations in Three-Dimensional Space" was set as one of the seven Millennium Prize problems by the Cray Mathematics Institute in the United States.

It can be said that whoever can study this problem clearly, and find out and prove this general solution, will catalyze countless new mathematical tools, mathematical methods, and physical theories, leading the world of mathematics and physics to achieve great development!

At that time, basically the Nobel Prize in physics, the Marcel Grossman Prize, the Fields Medal, the Craford Prize, the Wolf Prize in Mathematics, etc., will be soft, let alone It is said that it will bring huge social and economic benefits and promote human civilization!
Knowing the difficulty and significance of this Navier-Stokes equation, when Qin Ke saw that the reward given by the system was "Exploration and Detailed Solution of the Nonlinear Partial Differential Equation 'Navier-Stokes Equation' ( "Part [-])", 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 explanation" can prove "the existence of smooth solutions of NS equations in three-dimensional space" and find out the general solutions of the equations, but with Qin Ke's incredibly rich understanding of this system Based on the understanding of the knowledge base, this knowledge rated as S-level must be shocking!

As long as you 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, let alone Qingmu and Beiyan University, Princeton University, which has always been known for its arrogance, will probably kneel down Begging him to study, oh no, it should be teaching!

However, Qin Ke quickly calmed down. Even if he had acquired this knowledge, he still had to be able to understand it!
At least one must have a very solid foundation in university physics and mathematics, and even a higher level of postgraduate and doctoral knowledge. Otherwise, if the knowledge is given to him, he will be blind if he doesn't understand it.

Even if you understand and research thoroughly in the future, if you want to publish it, you must have enough fame and the halo of a super mathematical genius, so that your published papers may be valued by the mathematics community, and will not arouse suspicion and procrastination. Go to slice dissection.

To this end, Qin Ke must continue his journey in mathematics competitions. IMO gold medals and even champions are indispensable. Physics competitions must also enter the world competitions, and professional papers in mathematics must also start up.

From this point of view, the system has been guiding him on the right path through tasks.

At least publish some academic-level mathematics papers first, and accumulating fame is a necessary first step.

In the future, if there is an opportunity, academic papers on physics must also be produced.

The competition and academic papers, both of which complement each other, can establish his status and image as a top mathematician and physicist in the future, and it will be logical to publish a paper on the "Navier-Stokes Equation" at that time.

After looking up at the starry sky and the future, Qin Ke turned his attention back to the task itself—to publish his first academic paper, and he had to publish a professional academic paper on "mathematical analysis" in a national academic journal.

But academic papers...

I have only written [-] words in composition, let me write academic papers?

Qin Ke fell into deep thought, and then decided to ask Professor Shi Cunyuan in the front row for advice.After all, this is a postgraduate tutor of a prestigious university. Although Yuanzhou University cannot compare with Qingbei, it is also the best university in Huahai Province, ranking 985 and 211.

Shi Cunyuan's academic level in mathematics is beyond doubt.

Thinking of this, Qin Ke gently tapped the seat in the front row: "Mr. Shi, is it convenient? I have a question to ask you."

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