Chapter 271 Communication and Inspiration (Asking for Monthly Votes)

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 Xu Chuan has published in the past, he has covered quite a lot in various fields of mathematics, so much that he can be compared to Terence Tao.

In addition to mathematics, he is also deeply involved in physics, astronomy, materials and other fields.

Although he mainly relied on mathematical methods to win the Nobel Prize in Physics, it is impossible to master the calculation methods without in-depth understanding of the corresponding astrophysical knowledge that he is not familiar with.

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

Even if prenatal education begins in the womb, it is difficult to imagine how it is learned.

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

But compared to this one, it's nothing.

This freak had already won the Fields Medal and the Nobel Prize at the age of twenty-two, and stood at the pinnacle of the entire mathematical world and even the scientific world.

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

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

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

Theoretically speaking, the mist on this teapot floats upward, and the shaped water mist gradually disperses and disappears in the air. Is it not a fluid with a very low viscosity coefficient?

Staring at the dissipating fog on the teapot, an idea flashed through his mind.

Sometimes, the study of fluids or turbulence is like the fog on this purple clay teapot. Starting from the root of the teapot, it rises in an orderly and stable manner, then begins to spread and become chaotic due to external interference in the middle, and then finally loses completely. Control completely disappears into the air.

Although from a physical level, the dissipated fluid still exists, it can no longer be described mathematically.

From initially predictable to ultimately completely out of control, from motion that can be deduced using mathematical formulas to impossible to even record with data, this is turbulence.

However, turbulence is not boundless.

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

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

Perhaps, we can construct multiple linear operators in three-dimensional space, satisfy the standard orthogonal basis matrix for any vector, and use the Hilbert method to find soliton solutions to nonlinear equations.

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

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

He was very familiar with this state, and he knew very well that the other party might have had inspiration or an idea. After looking at it with interest, he did not continue to disturb him, and waited silently.

On the side, Wei Yong was about to step forward when he was stopped by his instructor Qiu Chengtong. The silence movement of his fingers in front of his lips made him understand instantly, and he carefully shrank into the corner, looking at Xu Chuan who was deep in thought without even daring to say anything. Panting, trying his best to reduce his presence, for fear that his presence would disturb the other person's thinking.

The atmosphere in the office fell into an eerie silence for a while.

Xu Chuan pondered deeply and did not come back to his senses until the rising mist disappeared as the temperature in the teapot dropped.

Looking at Qiu Chengtong who was waiting quietly on the side, he smiled sheepishly and said, "Sorry, I just got distracted."

Qiu Chengtong smiled nonchalantly, stood up, took away the purple clay pot, drained the tea and brewed another pot, then asked, "Do you have any ideas?"

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

Qiu Chengtong asked curiously: "Can we chat?"

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

He briefly talked about the inspiration he had just received. Sometimes, going out for a walk can really benefit people a lot.

If he were in his own villa in Jinling, it would be impossible to get inspiration from the steaming mist of tea given his character who rarely drinks tea. But here with Qiu Chengtong, he has not yet started to communicate with the other party. , something has been gained.

After listening to Xu Chuan's narration, Qiu Chengtong pondered for a moment and then said: "This is indeed a very good idea. From a computational point of view, this path should be feasible. However, I recommend replacing the bilinear operator with Compared with linear transformation, the former still has limitations, especially when facing some special spaces, the ability of bilinear operators may not be enough. "

Xu Chuan thought for a while, nodded, and said: "Indeed, but bilinear operators also have unique advantages. For example, the displacement of bilinear operators in vector space has symmetrical properties. In special spaces, such as squares, It is quite suitable for spaces such as ellipses and circles.”

"Maybe 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 for ultra-high temperature plasma turbulence, the variation is too large. Today's computer performance and intelligence may not be able to do it, even using supercomputers may not be feasible."

"You should know that when a mathematical model has too many variables in operation, it will be a computing task that even supercomputers cannot complete."

He already knew Xu Chuan's intention, so after thinking about it, he reminded him of this problem from an engineering perspective.

Xu Chuan pondered for a while and said, "What you said makes sense. If the model operation is too complicated, the computing power requirement is too high, especially for the plasma turbulence in the chamber of a controlled nuclear fusion reactor. A little disorder will easily lead to a large increase in the amount of calculation."

It must be said that Qiu Chengtong's ability is indeed terrifying. He pointed out the problem in his idea.

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 Harvard University's history to serve as a professor of both the Department of Mathematics and the Department of 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 three-dimensional image processing. He can be said to be a top expert in both theory and application.

It is a blessing for the country that such a talent is now returning 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 sunset fell on them through the glass window.

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

This exchange was very beneficial to both him and Qiu.

The two truly top mathematicians opened their hearts and exchanged their respective insights in the field of partial differential equations. This was a collision of sparks of wisdom, which may merge into a larger firework 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 a grand goal that is almost impossible to achieve in one step.

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

In the study, Xu Chuan took a stack of manuscript paper and pen, and sat at the desk in deep thought.

Next to him, the laptop and desktop screens that had been opened had web pages and papers opened one after another.

These are all preparations before starting formal work.

Whether writing a paper or proving a difficult problem, it is often necessary to quote or find various materials.

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

"Study on the nonlinear exponential stability and overall existence solution of compressible Navier-S in three-dimensional space!"

After writing a line of title, he began to write an introduction for the entire proof.

[Introduction: The motion equation of viscous fluid was first proposed by Navier in 1827, and only the flow of incompressible fluid was considered. Poisson proposed the motion equation of compressible fluid in 1831. Saint-Venant in 1845, Stokes in 1845]

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

[.]

[The compressible viscous N-S equation consists of three conservation equations: the mass conservation equation, the momentum conservation equation, and the energy conservation equation. And three unknown functions are included: (v (x, t), u (x, t), θ (x, t)), representing the specific volume (inverse of density), velocity, and absolute temperature of the fluid, respectively. Next, the existence and uniqueness of the solution of the initial boundary value problem of the equation system are discussed.]

[At present, all discussions are on bounded domains.]

[Therefore, can a finite domain with Dirichlet boundary conditions be given, and in three-dimensional space, the Navier-Stokes equation has real solutions, and the solutions are smooth? 】

PS: There will be another chapter in the evening, please vote for me.