Great Country Academician

To be honest, Qiu Chengtong really couldn't figure out how the monster in front of him learned it.

Algebraic geometry, differential equations, partial differential equations, functional analysis, topology, manifolds.

Judging from the mathematics papers that Xu Chuan sent out in the past, he has involved quite a lot in various fields of mathematics, which is comparable to Terence Tao.

In addition to mathematics, he also has deep involvement in physics, astronomy, materials and other fields.

Although he won the Nobel Prize in Physics mainly relying on mathematical methods, if he does not have a deep understanding of the corresponding astrophysical knowledge, it is impossible to master the calculation methods.

But if he remembered correctly, the person in front of him was only twenty-two years old this year.

Even if prenatal education starts in the womb, it is hard to imagine how to learn.

To be honest, he, Qiu Chengtong, also considers himself a genius in the mathematics field. When he was 22 years old, he studied under Chen Shiingshen and graduated from the University of California, Berkeley with a doctorate. He is already very good in the mathematics field.

But compared to this one, it's really nothing.

This freak had already won the Fields Medal and the Nobel Prize at the age of 22, standing at the pinnacle of the entire mathematics world and even the science world.

In the office, Wei Yong quickly brought over a pot of hot water after boiling it.

Qiu Chengtong personally took out the treasured tea leaves from the cabinet, picked up the kettle and made a pot of hot tea.

The hot mist curled up on the purple sand pot, Xu Chuan stared at the mist and fell into deep thought.

Theoretically speaking, the mist on the teapot is misty upwards, and the shaped mist gradually dissipates and disappears in the air. Isn't it a fluid with a very low viscosity coefficient?

Staring at the mist dissipating from the teapot, a thought flashed through his mind.

Sometimes, the study of fluid or turbulence is like the mist on the teapot. It starts from the root of the teapot, rises in an orderly and stable way, and then begins to diffuse and become disordered due to external interference, and finally loses completely. Control, completely disappeared into thin air.

Although from a physical perspective, the dissipated fluid still exists, but it can no longer be described by mathematics.

From the initially predictable to the eventual complete loss of control, from the motion that can be derived mathematically to the point where it cannot even be recorded with data, that is turbulence.

However, turbulence is not infinite.

Just like the water mist in front of you, human breathing, the breeze outside the window, and the impact of alternating cold and heat on the air can all interfere with the water mist.

Staring at the hazy water mist in front of him, Xu Chuan's mind became active.

Perhaps, multiple linear operators can be constructed in the three-dimensional space, satisfying the orthonormal basis matrix for any vector, and using the Hilbert method to find the soliton solution of the nonlinear equation.

A vague train of thought gradually became clear in his mind, but no one could be sure what the end was.

On the opposite side of the desk, Qiu Chengtong was just about to pick up the purple clay pot to share tea when he noticed Xu Chuan who was staring at the purple clay pot in deep thought.

He is very familiar with this state, and he knows that the other party may have an inspiration or idea. After looking at it with interest, he didn't continue to disturb him, and waited silently.

On the other side, just as Wei Yong was about to step forward, he was stopped by his instructor Qiu Chengtong. The silent movement of his fingers in front of his lips made him understand instantly, and he shrunk cautiously to the corner, looking at Xu Chuan who was in deep thought. Panting, try to reduce your sense of existence, for fear that your existence will disturb the other party's thinking.

In the office, the atmosphere fell into an eerie silence for a while.

Xu Chuan pondered until the rising water mist disappeared as the temperature in the teapot dropped.

Looking at Qiu Chengtong who was waiting quietly, he smiled embarrassedly and said, "Sorry, I was distracted just now."

Qiu Chengtong smiled indifferently, got up and took away the purple sand pot, let go of the tea in it and brewed a pot again, and asked: "Is this an idea?"

Xu Chuan nodded and said, "Well, I was a little inspired, so I thought about it."

Qiu Chengtong asked curiously: "Can we talk?"

Xu Chuan: "Of course, it's mainly about some control calculations for external disturbances and predictions."

He briefly talked about the inspiration he just got, and sometimes going out for a walk can really benefit people a lot.

If it was in Jinling's own villa, with his character of hardly drinking tea, it would be impossible to get inspiration from the steaming mist of tea, but with Qiu Chengtong, he hasn't started communicating with the other party yet. , has already gained something.

After listening to Xu Chuan's narration, Qiu Chengtong pondered for a while and then said: "This is indeed a very good idea. From a calculation point of view, this road should be feasible. But I suggest replacing the bilinear operator with Compared with the latter, the linear transformation still has limitations of the former, especially when facing some special spaces, the bilinear operator may not be capable enough.”

Xu Chuan thought for a while, nodded, and said: "Indeed, but bilinear operators also have unique advantages. For example, the permutation of bilinear operators in vector spaces has a symmetrical property. In special spaces, such as square , ellipse, circle and other spaces are quite suitable.”

"Perhaps they can be mixed together?"

Qiu Chengtong shook his head and said: "Mathematically speaking, this should be feasible, but if you want to use this to build a control model for turbulence, it may not work."

"Especially in ultra-high temperature plasma turbulence, the amount of change is too large, and today's computer performance and intelligence may not be able to achieve it, even with supercomputers."

"You should know that when the variables in a mathematical model are too large, it will be a calculation task that even supercomputers cannot complete."

He already knew the purpose of Xu Chuan's visit, so after thinking about it for a while, he reminded this question from an engineering point of view.

Xu Chuan pondered for a while, and said: "You are right. If the calculation of the model is too complicated, the requirements for computing power will be too high, especially for the plasma turbulence in the controllable nuclear fusion reactor chamber. There is a little disorder, and it is easy to increase the amount of calculations."

It has to be said that Qiu Chengtong's ability is indeed terrifying, and he pointed out the problems in his conception.

His scientific research ability is not only in mathematics, but also in physics and engineering.

He was a tenured professor of physics at Harvard University and the only person in the history of Harvard University who concurrently served as a professor of mathematics and physics.

When he was the director of the "Center for Mathematical Sciences and Applications" at Harvard University, Qiu's contributions involved cybernetics, graph theory, data analysis, artificial intelligence, and 3D image processing. Top cow.

It is a blessing for the country that such a talent is returning home to contribute to the country.

In the office, Xu Chuan and Qiu Chengtong kept exchanging their views and ideas in the field of partial differential equations until the evening sun fell on them through the glass window.

After bidding farewell to Qiu Chengtong, Xu Chuan returned to Jinling.

This exchange, both for him and for Qiu, has benefited a lot.

Two truly top mathematicians opened their hearts and exchanged their respective insights in the field of partial differential equations. This is the collision of sparks of wisdom, or they will merge into a larger spark to illuminate the seemingly chaotic fog.

Back in Jinling, Xu Chuan temporarily put aside other work and locked himself in the villa.

Establishing a mathematical model for the ultra-high temperature plasma turbulence in the chamber of a controlled nuclear fusion reactor is an ambitious goal, and it is almost impossible to achieve it in one step.

But now, he has enough qualifications and ability to open up this road a little further.

In the study room, Xu Chuan fetched a stack of manuscript paper and pens, sat at the desk and meditated.

Next to it, there are webpages and papers opened on the screens of laptops and desktops that have been turned on.

These are the preparations before starting the official work.

Whether it is writing a paper or proving a difficult problem, it is often necessary to cite or search for various materials.

In front of the desk, Xu Chuan contemplated for a long time, and finally raised his right hand. With the black ballpoint pen in his hand, he wrote a line of title on the blank A4 paper.

Research on nonlinear exponential stability and global existence solution of compressible Navier-S in three-dimensional space! "

After writing a one-line title, he began writing the introduction for the entire proof.

[Introduction: The equation of motion for viscous fluids was first proposed by Navier in 1827, which only considered the flow of incompressible fluids. Poisson proposed the equation of motion of compressible fluid in 1831. saint-venant in 1845, stokes in 1845]

[The Navier-Stokes equation (Navier-Stokes equation) is a motion equation describing the conservation of momentum of a viscous incompressible fluid, referred to as the N-S equation. The N-S equation summarizes the general law of viscous incompressible fluid flow, so it has special significance in fluid mechanics.]

【.】

[The compressible viscous N-S equation consists of three conservation equations: mass conservation equation, momentum conservation equation, and energy conservation equation. And include three unknown functions: ( v ( x, t ), u ( x, t ), θ( x, t )), which respectively represent the specific volume (reciprocal of density), velocity, and absolute temperature of the fluid. Next, we discuss the existence and uniqueness of the solution to the initial boundary value problem of the system of equations. 】

[For now, all discussions are on bounded domains. 】

[Therefore, is it possible to give a finite bounded domain and a Dirichlet boundary condition, in three-dimensional space, the Navier-Stokes equation has a real solution, and the solution is smooth? 】

PS: There is another chapter in the evening, asking for a monthly pass.