Section 257

“Finally, through energy estimation, we prove the consistent boundedness of the approximate solution sequence (Un), and using the compact embedding theorem, we can complete the proof of the existence of the solution.”

"As for the smoothness of the solution, it is already very simple at this point."

“What we mainly utilize here is high-order energy estimation and regularity improvement.”

"First using the properties of Shaw space, we perform high-order energy estimation."

【d/dt∥u∥^2Hs+2ν∥u∥Hs2≤C(∥u∥^2Hs+∥f∥^2Hs)】

"Then we will further improve the regularity of the solution through the embedding theorem, and finally prove the smoothness of the solution."

"That's it, the proof is complete."

After Xiao Yi heavily marked a dot on the blackboard, he turned around and looked at the audience present.

"At this point we have undoubtedly proven that the flow of liquid is smooth and every liquid molecule is continuous."

"They won't do anything we can't understand, and they won't sit quietly in this cup and suddenly explode."

Xiao Yi opened the lid of the water glass in his hand, took a sip, and said with a smile: "In the same way, they will not explode after entering my stomach."

"All in all, the behavior of fluids can be predicted."

Having said this, he also felt something: "In the same way, I think the plasma flow can also be predicted."

Then he bowed slightly: "Okay, my narration is finished. Now if you have any questions, you can ask me questions."

Soon, quite a few people raised their hands.

Xiao Yi named a middle-aged man with a foreign face who looked like a professor.

He stood up, took the microphone handed over by the staff, and asked: "Hello, Professor Xiao, I am Jimmy Lawrence from the Department of Physics at MIT. May I ask how Sobolev space and Besov space define Xiao space? What role did the protagonist play? I found that you focused on these two spaces in your narration.”

Xiao Yi nodded: "That's a good question."

"The reason why we focus on Sobolev space and Besov space is mainly because of their respective advantages. Sobolev space provides good regularity and energy estimation, while Besov space is very effective for dealing with local smoothness and small-scale structure. Combining these two space, we can not only ensure the overall regularity when dealing with the solution of NS equations, but also capture the local complexity and details. "

"Of course, just saying this may not be very intuitive, so I will simply demonstrate it to you mathematically."

"Now we simply substitute Sobolev space and Besov space into Xiao space, and we can get..."

[X={u∈H^s(Ω)∩B ^s_(p, q)(Ω):∥u∥X<∞}

"Among them, ∥u∥X is a suitable norm that combines two spatial norms. Under such analysis, we can..."

"Finally, it can be seen that with the combination of these two spaces, the Xiao space has good regularity and overall energy estimation, as well as local smoothness and the ability to capture small-scale structures."

"Do you have any more questions?"

Xiao Yi turned around and looked at Professor Lawrence from MIT.

Professor Lawrence was already a little confused.

He is just a physics guy, so he really doesn’t need an introduction from a mathematical perspective!

Now, Xiao Yi has finished explaining, but he hasn't even finished reading the first line of the formula.

But at this moment, facing so many looks, he could only nod his head and said, "Thank you for your explanation, I understand..."

Then he sat back.

Xiao Yi nodded slightly, and then looked at the others: "Any more questions?"

This time, there were far fewer people raising their hands.

I don’t know if it’s because their problems are the same as this Lawrence’s, or because they’re afraid that Xiao Yi will directly show them a mathematical derivation when he comes up.

Soon, Xiao Yi answered five questions in a row, and no one raised their hands anymore.

And just when everyone thought that no one would raise their hands again, Terence Tao, who was sitting in front, raised his hand at this time.

There are still many people who know him, and many people immediately became interested and curious about what questions Terence Tao would ask.

The questions asked by such a great expert should not be simple questions, right?

On the stage, Xiao Yi also raised his eyebrows, and then said with a smile: "Professor Tao, please ask a question."

Tao Zhexuan smiled, took the microphone, and said, "Well, actually, I just have a question. How did the ideas in your mind come up when you deduced Xiao's space? This is the only thing I haven't understood until now. question."

He had read the paper, which was very detailed, and the current report had already explained some of the things he wanted to know before.

For example, the data analysis method of explosive trend theory.

But this was the only problem he couldn't figure out.

And when he asked this question, those in the audience who understood what he said were stunned.

They never expected that Terence Tao's final question would be so simple.

What is Xiao Yi's thinking?

What's there to ask?

However, there are still many top scholars who can understand what Terence Tao meant by asking this question.

It is very meaningful to study the ideas of other scholars.

Top scholars often look at other scholars' papers and reports to think about each other's research methods.

But here's what surprised them.

Even a math expert like Terence Tao couldn't figure out Xiao Yi's idea?

Of course, Xiao Yi on the stage was also stunned when he heard this question.

However, he then smiled and said: "My idea... is not that complicated."

"Since fluids are so complex, it would be nice to use more detailed descriptions to explain their complexity."

"That's it."

Tao Zhexuan was shocked, and after a moment, he sighed: "As expected of you."

"Thank you for your answer, I understand."

Then he sat back.

Xiao Yi smiled at him, then looked at the others and asked, "Any more questions?"

Not a single hand was raised.

"Then, my report meeting ends here."

“Thank you everyone for attending.”

Bow slightly.

The originally silent assembly hall was overwhelmed by the wave of applause.

Chapter 224 Interview with Time Magazine

This is how the report meeting ended.

For the vast majority of people present, although they were still a little confused about what Xiao Yi said, it did not prevent them from cheering for this lecture that was destined to be recorded in the history of mathematics and physics.

Thinking about it in the future, when they search for news related to NS equations on the Internet, they will probably see this description: [After Xiao Yi completed the proof, he held a report meeting in Huaguofei City, and at the end of the report meeting , received warm applause from the audience. 】

At that time, they can proudly say to others: "At the scene, it is not a table, nor a chair, nor a microphone, but it is in seat XX in row XX."

Probably because they still had some memories of this report, the warm applause continued for a long time, making Xiao Yi feel as if he was not here to give an academic report, but to give a concert.

What he just gave was not a report, but a music feast that lasted for nearly two hours. The applause was like hoping that he could perform an encore.

In the end, he had no choice but to clap along with the audience.

About two or three minutes passed before the applause gradually stopped.

Then, as the host, Bao Hexin also walked onto the stage again and said with a smile: "Okay, I also know that everyone is very excited at this time, but this report meeting has been going on for so long, It’s already lunch time.”

"We have prepared a sumptuous meal and tea break in the hotel next door. We also ask everyone to leave the conference hall in an orderly manner under the guidance of the staff and go to the hotel to dine. Believe me, the meal we have prepared today will never let you down. Everyone is disappointed!”

As soon as they heard about the tea break, the eyes of most people present lit up, and of course they were waiting to leave without saying a word.

However, many of the big guys sitting in front were naturally unwilling to leave like this. They walked up to the stage one after another and began to communicate with Xiao Yi, such as discussing the use of explosive trend theory and Xiao's space, and then And his final proof result, where it can be used, etc.

Of course, their discussion did not last long, after all, everyone was basically hungry.

"Okay, let's go to the restaurant and eat and talk. Speaking of which, I also want to know what has been prepared for this tea break."

Xiao Yi said to Tao Zhexuan and others with a smile.

Tao Zhexuan and other big names also smiled and nodded.

"Then let's go. I'm also very curious about what will be prepared for the banquet in Huaguo. I have read some strategies before coming here. I heard that there are some meat buns?"

Xiao Yi laughed and said: "Rougamo is a famous snack in Qin Province of China, and it is indeed very good. Of course, in our Hui Province, there is a dish called Huainan Beef Soup. I think you should not miss it. In addition, there are There are Huangshan Shaobing and the like, these things should be available later.”

He had heard that the chefs invited for this banquet were all top-notch chefs in the country, so there was basically no need to worry about the food.

Fefferman was surprised and said: "Oh! I didn't expect that you have different special foods in different regions?"

Xiao Yi nodded and gave this American who had never been to China a good introduction to the eight major cuisines.

Fefferman was amazed when he heard this, and finally couldn't help but sigh: "I've had enough of eating fried eggs and toast for breakfast, hot dogs for lunch, steak and pizza for dinner, and all kinds of burgers." ”

Xiao Yi shrugged and said: "The geographical environment is different, and the diet is naturally different. You can often eat steak, but here, steaks are relatively high-end meals."