Chapter 334: Give the Mathematics World a Shock (12)

In fact, the previous contents were not very obscure and difficult to understand. They were all basic equations. After all, everyone present was a math expert. It was just that they lacked an overall framework, that is, a basic conceptual theory. What Chen Xiaoxin is writing now is this framework theory.

As Chen Xiaoxin finished writing this line of formula, many experts and scholars present showed astonishment and were caught off guard. They were still confused about the previous content, but now, after seeing this new line of formula, the layers of fog were directly dispelled!
That's it!

The contents before that are all theorems, no wonder it is a bit difficult to understand. Now that the theory has been derived, everyone suddenly realizes it. Looking back at the previous content, there is a feeling of sudden enlightenment.

"As you can see." Chen Xiaoxin turned around and said to everyone present: "By weakening the nonlinear part of the NS equation, or strengthening the linear part, and then by discretizing or regularizing the spatial scale, it seems that there is a chance to get the overall solution of the NS equation."

“But it’s just a chance.”

Chen Xiaoxin paused and continued, "What I did was to relax the concept. The overall solution is not the ultimate goal of proving the NS equations. There are also spatial solutions and smooth solutions that need to be dealt with. This step is to pave the way for the next two problems. In order to ensure the spatiality and smoothness of the overall solution, convergence needs to be achieved under strong topology!"

finished,

Pointed to the last line of formula.

"In fact, the scaling argument basically requires us to obtain convergence in critical or subcritical topology, but the types of convergence that can be obtained are currently limited to very coarse topologies." Chen Xiaoxin pursed his lips and continued, "The ultimate problem is to control the unit scale solution of arbitrarily large scales."

“Here.”

"I think everyone should have a general idea of ​​it."

"That's right. We need to conduct research in a purely qualitative framework, not a non-quantitative framework." Chen Xiaoxin said seriously, "Then we will move on to the next question. I'm sure you have seen the non-disturbance tool, the mathematical tool for controlling deterministic non-integrable dynamic systems."

As soon as the words fell,
I walked to the new question board and quickly wrote down the math tool.
"This is based on stochastic partial differential equations. It involves stochastic analysis, Ito integral, functional analysis and topology, but please rest assured that I will explain it in detail." Chen Xiaoxin said leisurely: "The only non-perturbative deterministic limit I know of at present is the discovery of new monotonic quantities. In the past, they were always related to geometry, physics and nonlinearity."

"And in the system of equations."

"There is almost no available geometric structure." Chen Xiaoxin wrote new content on the question board.

"All right."

"let us start!"

Chen Xiaoxin stopped talking and concentrated on writing the proof process on the question board.

The huge conference hall was silent except for the crackling sound between markers and the answer board. Everyone stared at the huge display screen in front of them, watching the calculation process appearing line by line on it, with excitement and excitement between their brows.

“He’s so fast!”

Professor Foryo from the United States was already at the point of having his scalp tingling. Although the content of this part was not as puzzling as the previous ones, it still required careful analysis to understand the meaning behind it. But there was a problem that before he could understand one line of the formula, Chen Xiaoxin had already written five or six lines.

I can't keep up! He's too fast, my brain can't keep up with his pace.
Every time he tried to figure out the meaning behind a line of equation, Chen Xiaoxin would quickly write down several lines at an incredible speed, like a madman!
Sometimes Professor Foryo wondered if Chen Xiaoxin was actually thinking about what he was thinking when he wrote down these words? Or was his current behavior just a subconscious reaction, and he only needed to raise his hand to prove that the process would come automatically?
"indeed."

"My brain can't keep up." Professor Anderson beside him had a bitter look on his face and muttered to himself, "It's horrible."

the other side,
Mr. Qiu was watching the contents on the display screen with great interest. Although he had encountered similar problems, every time he understood the role of a line of formula in the entire proof process, the joy he felt made him deeply fascinated.

"Mr. Qiu?"

"Can you keep up with his pace?" Dean Chen of the School of Mathematics at Peking University asked cautiously.

Mr. Qiu shook his head and replied helplessly, "No. He wrote too fast. I could understand one line of equation, but he could write five or six lines of process. I have to say that his mathematical talent is so strong that it makes me ashamed."

"Hey"

Dean Chen sighed, turned his head and looked at Chen Xiaoxin's back, his brows full of resentment and bitterness, how close he was to getting him! Now, he has reached a height that even the whole world cannot reach.

Time slowly passes.
More than half an hour passed in the blink of an eye, and during this period, not even one person went to the toilet. They just sat there quietly, looking at the various complicated formulas that appeared on the LED display. Of course, it was not because their bladders were in good condition, but because they were afraid of missing out on the exciting parts.

The motion of fluids in the physical domain is driven by various properties such as velocity, pressure, temperature, density, and viscosity, taking into account physical phenomena such as combustion, multiphase flow, turbulence, and mass transfer. These properties vary greatly and can be divided into kinematic, transport, thermodynamic, and other miscellaneous properties.

Conceivable
How difficult is it to solve the NS equations?

This is also the reason for everyone to hold their urine. They would rather their bladder explode than miss every second here.

Chen Xiaoxin seemed to have sensed their thoughts, so at this moment, when he finished writing the last operator, he silently put down the pen in his hand, stepped back several steps, and stood there checking the contents on the question board.

For a time,

The emotions of everyone present were also aroused, and their eyes were filled with burning light.

"On the proof of non-perturbative tools."

"It's basically over here. Now let me talk about the difficulties." Chen Xiaoxin said.

In the following time, Chen Xiaoxin talked about his proof process. In fact, all these contents are in the paper, but the contents in the paper are simplified versions, not as detailed as they are now. Of course, it is not too detailed. Anyway, if you can understand it, listen, and if you don’t understand it, get out.

Another half hour passed
Chen Xiaoxin picked up a bottle of water, gulped down half of it, and said, "That's about it. Let's end it here. This afternoon we will focus on boundary problems and understanding pseudo-randomness. Welcome everyone. Once these two problems are explained, the proof of the existence of the solution to the NS equation will be concluded. In addition, I will announce something very important."

As soon as the words fell,
He just patted his butt and left.

"Hee hee hee"

"Husband, you are awesome!"

As Chen Xiaoxin's future wife, a petite and beautiful young woman rushed up to him immediately, gently took his arm, and said with a smile: "You are amazing. I love you so much!"

Chen Xiaoxin sighed and replied bitterly: "I am so tired. Can you let me have a good rest tonight? Don't bother me anymore."

"Yes Yes Yes."

"I sleep in my own house at night, is that okay?" Yan Xiaoxi rolled her eyes and said angrily, "You're thinking about sleeping in separate rooms before you even get married. It looks like I'll be a widow sooner or later!"

Chen Xiaoxin smiled awkwardly and replied helplessly: "You can't blame me for this. You seem to be hungry every day. How can my delicate body withstand your abuse?"

"roll!"

Yan Xiaoxi glared at him fiercely and said angrily: "Why can't I eat enough? Have you ever thought about this problem?"

Just as the two were bickering, Director Wang from the Department of Mathematics at Fudan University came over with a smile on his face and said excitedly, "Xiao Chen is excellent! It's perfect! Keep up the good work this afternoon. The key leaders are very happy."

In addition to experts and scholars in the field of mathematics, several leaders of Shenhai were present at this report meeting. If it were in the past, they would definitely give advice in various aspects, but the protagonist today happened to be Mayor Yan's future son-in-law Chen Xiaoxin, so he didn't dare to give any advice even if he was given ten courage. "By the way."

"There will be a celebration banquet tonight. You two must come!" Director Wang said, "Many leaders will be there."

Chen Xiaoxin has always disliked these things. Instead of focusing his energy on these things, he would rather focus on research. But then again, he can't not do it. After all, he is a professor at Fudan University, and the son-in-law of Mayor Yan. He has to do some face-saving work.

"Um"

"understood."

Chen Xiaoxin nodded and didn't say much.

In the following time, Chen Xiaoxin met many mathematicians, but as it was close to dinner time, everyone just exchanged a few simple greetings and went to the restaurant separately.

Fudan University specially created a cafeteria and arranged a buffet to entertain these mathematicians from home and abroad.

Although Fudan University spent a lot of money for this day, the school's reputation has been thoroughly established, not only in China but also abroad. Whenever the issue of NS equations is mentioned, everyone will think of Chen Xiaoxin's explanation of those four questions at Fudan University's lecture.

Time slowly came to the afternoon, and the lecture hall was full of people again. There seemed to be even more people than in the morning, and the back was almost full of people standing.

Everyone was anxiously waiting for the academic report in the afternoon. Meanwhile, Chen Xiaoxin was in a small cubicle in the conference hall, writing and drawing on a notebook.
"Fool."

"A lot of people came again in the afternoon."

Yan Xiaoxi found him and said helplessly, "The back is full of people."

"Oh"

Chen Xiaoxin responded disapprovingly.

"correct."

"Have you proved the spatial solution and the smooth solution?" Yan Xiaoxi asked.

Chen Xiaoxin was stunned for a moment, looked at the little fairy beside him, and asked curiously: "How did you know?"

"Humph."

"I am your wife!"

Yan Xiaoxi rolled her eyes and replied softly, "After the overall solution is proven, the subsequent spatial solution and smooth solution are just a matter of time. I don't think you will give up such an important result to others."

"and"

"And you've been acting a little weird these past two days." Yan Xiaoxi said coquettishly, "So I guess you're probably solving the next two proofs of the NS equation."

"Tsk, tsk, tsk."

"As expected of my beloved wife, you know everything." Chen Xiaoxin did not hide anything and said with a smile: "I have completely proved the NS equation and will announce it today."

At this moment, Yan Xiaoxi was only filled with pride. She used to be jealous, but now she had accepted the reality. Although she could not defeat him in mathematics and physics, he was no longer her opponent in bed at night.

In the blink of an eye.
Chen Xiaoxin appeared in the conference room, and the originally noisy lecture hall became extremely quiet at this moment.

“Let’s continue.”

“Here is the explanation of the border problem.”

Chen Xiaoxin didn't bother to say hello. He just picked up the pen and started writing frantically on the question board.

In fact, the last two questions are quite simple and only need to be explained. Especially for the boundary problem, many researchers transform the boundary problem into an abstract form. Although they can create an abstract object of a generalized solution, they will encounter all super-boundary problems when actually controlling the regularity of the generalized solution.

Chen Xiaoxin has adopted a new method to solve this problem, limiting the existence of super boundaries. Here we have to mention the tools he developed.
Just five minutes.
Chen Xiaoxin completed the supplement of non-disturbance tools. To be precise, it was a patch.

"hiss--"

“Just a supplement.”

The bearded professor from Princeton felt his scalp tingle when he saw the patch instructions. It was hard to imagine that the boundary problem that had been a headache for mathematicians all over the world could be solved with just a patch in Chen Xiaoxin's hands.

But Chen Xiaoxin did not stop. He came to the new question board and raised his hand to write the proof of the last question.

The NS equation possesses incredible randomness, but it is actually very difficult to express this concept in a mathematical model. Chen Xiaoxin can only describe the characteristics of the NS equation through pseudo-randomness.

The so-called pseudo-randomness is essentially a result that should be random but is not random.

of course,

This part is not the point.

Chen Xiaoxin only went a little deeper and completed an empty framework, because this part of the content does not affect the proof of the NS equation, it is just icing on the cake.

As Chen Xiaoxin completed the last line of content.

As he slowly put down the marker in his hand, it meant that the existence of the solution to the NS equation had been proved by him.

now,

There was a state of fearful silence in the venue.

You could even hear a pin drop.

Chen Xiaoxin turned around and looked at the crowd of mathematics experts from home and abroad in front of him. He cleared his throat and then slowly said:

"Then what's next"

"I will prove the existence of spatial solutions and smooth solutions!!"

Ah!
Then let’s give the mathematics community a little shock!

(End of this chapter)