Speaking from the heart, 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 mathematical papers sent by Xu Chuan in the past, he has a lot of involvement in various fields of mathematics, so much that it can be compared to Tao Zhexuan.

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

Although he won the Nobel Prize in Physics mainly by mathematical methods, it is impossible to complete the calculation method without in-depth knowledge and unfamiliar knowledge of the corresponding astrophysics.

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

Even if prenatal education begins in the mother's womb, it is difficult to imagine how to learn.

To be honest, he Qiu Chengtong also thinks that he is a genius in the field of mathematics, and when he was twenty-two years old, he studied under Chern Shiingshen and graduated from the University of California, Berkeley, and got a doctorate, and he is already very good in the field of mathematics.

But it's nothing compared to this one.

At the age of twenty-two, this freak had already won the Fields Medal and the Nobel Prize, standing at the pinnacle of the entire mathematical community and even the scientific community.

.......

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, lifted the kettle and brewed a pot of hot tea.

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

Theoretically speaking, the mist on this teapot is ethereal upward, and the tangible water mist gradually dissipates and disappears into the air, so isn't it a fluid with a very low viscosity coefficient?

Staring at the dissipating mist on the teapot, a thought crossed his mind.

Sometimes, the study of fluids or turbulence is like the mist on the purple clay pot, starting from the root of the teapot, rising in an orderly and steady manner, to spreading and disordered by external interference in the middle, and finally completely out of control and completely disappearing into the air.

Although the dissipated fluid still exists on a physical level, it is no longer mathematically describeable.

From what can be predicted at first to a complete loss of control at the end, from motion that can be deduced mathematically to something that cannot even be recorded with data, this is turbulence.

However, turbulence is not endless.

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

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

Perhaps, it is possible to construct multiple linear operators in three-dimensional space, satisfy the standard orthogonal basis matrix for any vector, and use the Hilbert method to find the soliton solution of the nonlinear equation........

A model lake's idea gradually became clear in his mind, but what the end was, no one could be sure.

........

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

He was very familiar with this state, and he knew very well that the other party might have an inspiration or idea, so he didn't continue to bother with interest after looking at it with interest, and waited silently on the side.

On the side, Wei Yong just wanted to step forward, but was stopped by his mentor Qiu Chengtong, the silent action of his fingers in front of his lips made him understand instantly, and he cautiously shrank into the corner, looking at Xu Chuan, who was deep in thought, he didn't dare to breathe, and tried his best to reduce his sense of existence, for fear that his existence would disturb the other party's thinking.

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

Xu Chuan pondered, and did not come back to his senses until the mist rising from the bird disappeared as the temperature in the teapot decreased.

Looking at Qiu Chengtong, who was waiting quietly, he smiled embarrassedly and said, "I'm sorry, I just got distracted." ”

Qiu Chengtong smiled indifferently, got up and took the purple clay pot, put down the tea in it and brewed it again, and asked, "Is this an idea?" ”

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

Qiu Chengtong asked curiously, "Can you talk?" ”

Xu Chuan: "Of course, it is mainly some control calculations for external interference, as well as ....... in prediction."

He briefly described the inspiration he had just received, and that sometimes it can be very beneficial to go out and walk.

If it was in his own villa in Jinling, with his character of almost not drinking tea, it could be impossible to get inspiration from the steaming mist of tea, but here in Qiu Chengtong, he had already gained something before he began to communicate with the other party.

After listening to Xu Chuan's statement, Qiu Chengtong pondered for a while and then said: "This is indeed a good idea, and from a calculation point of view, this path should be feasible." However, I recommend replacing the bilinear operator with a linear transformation, which has the limitations of the former, especially in the face of some special spaces, and the ability of the bilinear operator may not be enough. ”

Xu Chuan thought for a while, nodded, and said, "Indeed, but bilinear operators also have unique advantages, such as the symmetrical nature of the displacement of bilinear operators in vector space, which is quite suitable in special spaces, such as squares, ellipses, circles, etc. ”

"Maybe you can mix them up?"

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

"In particular, the turbulence of ultra-high temperature plasma is too variable, and the performance and intelligence of today's computers may not be able to do it, even if it is not feasible to use a supercomputer."

"You should know that when a mathematical model is operating with too large variables, it will be a computational task that even supercomputers can't do."

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

Xu Chuan pondered for a moment and said: "What you said makes sense, if the model operation is too complicated, then the requirements for computing power are too high, especially for the plasma turbulence in the chamber of the controllable nuclear fusion reactor. ”

I have to say that Qiu Chengtong's ability is indeed terrifying, and he pointed out the problems in his ideas with a sharp point.

His scientific abilities are not only mathematical, but also physical and engineering.

He was a tenured professor of physics at Harvard University and the only person in Harvard's history to hold both a professor of mathematics and a professor 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 3D image processing.

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

........

In the office, Xu Chuan and Qiu Chengtong constantly exchanged their views and thoughts 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 has benefited him a lot as well as for Qiu.

Two truly top-notch mathematicians open their hearts and exchange their insights in the field of partial differential equations, a collision of sparks of wisdom that may merge into a larger spark to illuminate the seemingly chaotic fog.

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

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

But now, he has the qualifications and ability to take it a step forward.

In the study, Xu Chuan took a stack of manuscript paper and pens and sat at the desk in contemplation.

Next to it, the laptop and desktop monitors that have been opened are open with web pages and papers.

These are all preparations before the start of the official work.

Whether it's writing a paper or proving a problem, you often need to cite or look up various sources.

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

"A Study on the Nonlinear Exponential Stability and Global Existential Solution of Compressible Navier-S in Three-Dimensional Space!" 》

After writing down a line of headings, he began to write the introduction to the entire proof.

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

[The Navier-Stokes equation is an equation of motion that describes the conservation of momentum in viscous incompressible fluids, referred to as the n-s equation.] The n-s equation summarizes the universal law of the flow of viscous incompressible fluids, so it has special significance in fluid mechanics.....】

【......】

The compressible viscosity n-s equation consists of three conservation equations: the mass conservation equation, the momentum conservation equation, and the energy conservation equation. There are three unknown functions: ( v ( x, t ), u ( x, t ), θ ( x, t )), which represent the specific volume (the reciprocal of density), velocity, and absolute temperature of the fluid, respectively. Next, the existence of the solution to the initial boundary value problem of the system of equations, and the uniqueness problem, are discussed. 】

[For now, all discussions are bounded.] 】

[Therefore, is it possible to give a finite bounded field with a dirichlet boundary, and in three-dimensional space, the OKES equation has a real solution and the solution is smooth?] 】

.......

ps: There is one more chapter in the evening, ask for a monthly pass.