I just want to be a quiet scholar

Chapter 476 New Developments in NS Equations

Shen Nuofei will have a full moon tomorrow, and today is just the day before the start of school in colleges and primary and secondary schools across the country.

At the request of relevant departments, elementary and middle school students across the country will watch the program "Big Class for the Beginning of School" at 8 o'clock tonight.

This year's "Back to School Class" is different from previous years. At 8:[-] p.m., "Back to School Class" starts on time without commercial breaks.

The warm-up team was not the heavily made-up entertainment draft singers, but the Chinese team, the runner-up of the World University Games men's basketball team.

The boys of the basketball team come from various colleges and universities across the country. In the men's basketball semi-finals of the just-concluded Universiade, they were 16 points behind in a difficult situation, relying on tenacious fighting spirit and impeccable teamwork, they staged a shocking reversal. Knock out the strong team Russia, enter the final historicly, and harvest a precious silver medal.

The Chinese college men's basketball team played vigorously, showing the masculinity of Chinese youth, and moved the whole of China.

The returning Chinese men's college basketball team introduced themselves at the beginning of "The Big Class". They are all college students, some of whom are studying materials, some are studying mechanics, and some are studying law.

Then the program played a set of VCR, which was a wonderful collection of famous Chinese scholars.

Physicists keep breaking the record of quantum entanglement, astronomers build national treasures to explore the universe, writers pour ink and paint their souls, and mathematicians solve century-old problems with high spirits.

Shen Qi was holding his daughter in front of the TV and watching "The Big Class for the Beginning of School". The mathematician on the TV screen was him.

Accepting patriotic education and science education started from a baby, Shen Qi is very satisfied with this year's program: "That's right, this is the real school education."

After the program was broadcast, no one complained about it among parents across the country, they all liked it.

The next day, school started.

Shen Qi organized a full moon wine for his daughter today, and invited a few relatives and friends to the banquet.

Zhou Yuan brought a bunch of gifts over, including milk powder, baby clothes, and dolls, all in a complete range.

"Niece Nuofei, I wish you a healthy growth." Zhou Yu'an said to Shen Nuofei.

Shen Nuofei smiled and didn't speak. She was developing relatively quickly. She would smile at things she thought were interesting at the age of one month, but she couldn't laugh out loud. It would take another month or two to make a laugh.

Xiao Junlong gave a piece of jade, saying that this jade has a lot of background and is suitable for girls to wear: "Xiao Nuofi, beautiful jade matches beauty."

The one-month-old baby couldn't laugh out loud, but could cry aloud. Shen Nuofei burst into tears, and Xiao Junlong's appearance scared her.

Ouye's best friend Xiao Lian gave him a baby hat.

Shen Nuofei laughed again, she would laugh when she saw normal-looking men and women, very cute.

Witten came to China a few days ago, and this time he returned to the United States to rest for more than two months.

Wei Teng, who went to do as the Romans did, gave a red envelope of 1000 RMB, which is really nice.

After finishing the full moon wine, Shen Qi, Wei Teng, Zhou Yu'an, and Xiao Junlong came to the center to discuss important matters.

Shen Qi said: "Zhou Yu'an has done very well recently. He proved the corner principle, and obtained a set of important data about the NS equation through the partial differential equation infinite flow algorithm. Zhou Yu'an, please tell me."

Zhou Yu'an played the PPT and began to explain: "According to Professor Wei Teng's algorithm framework and Professor Shen's supplementary improvement, I have obtained the following inferences."

Four sets of formulas are displayed on the screen:

(1) uj/t+Σukuj/xk=△uj-p/xi+fj, (t, x) ∈ Ω, i=1, 2, 3; divu=Σuk/xk=0, (t, x) ∈ Ω
(2) u(t,x)∣t=0=0
(3) u(t,x)∣xk=-π=u(t,x)=π,u/xk∣xk=-π=u/xk∣xk=π,k=1 ≤t≤a
(4) ∫Qp(t, x) dx=p0, p0=const>0
"The problem of the NS equation, we transform it into the problem of finding the velocity vector and scalar function at the point x ∈ Ω and the time t ∈ (0, a)." Zhou Yu'an switched the PPT to the next page.

This page writes a corollary: "Corollary 1: For f∈L2(Ω), if we find the solution of formulas (1)-(4), that is, we have solved the generalized solution of the NS equation, and this solution has universal significance. "

"Awesome, Lao Zhou!" Xiao Junlong stood up abruptly. Zhou Yu'an has not been able to retreat for the past few months, and he has done something extraordinary.

The previous derivation and proof work was all done by Zhou Yu'an. The only problem now, and the most critical one, is to find the solution of formulas (1)-(4) and prove this inference.

"It seems that there is nothing wrong with me." Wei Teng smiled and spread his hands, expressing his affirmation of Zhou Yu'an's efforts.

Shen Qi said: "So now we only need to do one thing. Zhou Yu'an made it very clear just now, to prove Corollary 1, which is to find the solution of formula (1)-(4). Then Zhou Yu'an, this last blow, It's up to you to do it."

"I can't figure it out." Zhou Yu'an shook his head, looked at Xiao Junlong: "Old Xiao, how about you?"

Xiao Junlong shook his head: "Old Zhou, you can't handle it, and I certainly can't handle it. The following things are no longer pure mathematical physics, partial differential equations, and fluid mechanics. They should also be dealt with using topological and functional tools. .Actually, Lao Zhou, we both have outstanding strengths, but we also have common weaknesses, that is, our professional scope is relatively narrow, and the comprehensive treatment still needs to be handled by Professor Shen and Professor Wei Teng."

The NS Equation project has advanced to this stage, and all four have contributed.

The current situation is that the two generals Zhou and Xiao have wiped out all the mobs, and the remaining big boss needs to be solved by the two big bosses.

The two big men looked at each other, that's all right, let's do it.

The NS equation project has entered the critical stage, and Shen Qi and Wei Teng have carried out a division of labor.

Wei Teng's thinking is clear, and he has a good view of the overall situation, but after all, he is old, and he is a bit struggling for high-intensity specific calculations.

The tedious and complicated derivations and calculations in the critical stage were performed by Shen Qi himself, and Wei Teng was responsible for checking the calculations, picking out faults, and finding loopholes.

After formulas (1)-(4) are expanded, a large number of partial differential and ordinary differential equations are derived, as well as more than a dozen definitions and lemmas that need to be proved.

In order to simplify the calculation, Shen Qi specially invented a new tool and discussed it with Wei Teng.

"From Lemma 2 to Lemma 9, the normal idea is to consider the case of u2, u3 to infinity, then we have to use Lemma 3 infinite times, the most troublesome thing is the non-negative monotonically increasing function, which means that our workload It will increase more than a hundred times."

"So I invented this new tool. It is a kind of processing method. It is established, simple and efficient." Shen Qi showed Weiteng the new method he invented. Let PN be the N-dimensional orthogonal projection calculation in H , then for any x∈H, when N→∞, PNx→x.

After Witten verification, the new tool satisfies the interchangeability of P and A, and can be used in the calculation proofs of Lemma 2 to Lemma 9 to simplify the calculation process and improve efficiency.

Even though the operation was simplified, the work continued throughout September, and Shen Qi did not calculate the generalized solution of the NS equation.

Regardless of whether he can solve the NS equation or not, Shen Qi gets home from get off work on time at 5 o'clock every day.

Today, when Shen Qi teased the two-month-old daughter, the daughter laughed.

"Nuofei, I know it's useless for you to laugh at me. You can't even solve the NS equation. How about I don't understand this equation for now. I'll leave it to you when you grow up, okay?" Shen Qi touched Touch the girl's pink face.

The daughter continued to laugh, drooling with laughter.

Shen Qi: "Girl, can you give me some hints?"

Shen Nuofei: "Giggle."

Shen Qi was quite pleasantly surprised: "Nuofei laughed out loud, and laughed out loud in two months!"

Seeing Shen Qi like this, Shen Nuofei couldn't stop laughing, this is a baby girl who loves to laugh: "Slightly, slightly, slightly."

"Slightly slightly slightly slightly, cycle boundaries?" Shen Qi suddenly realized, and her daughter said that cycle boundaries must be correct!
Shen Qi handed the daughter to Ouye: "The child's mother, hold the baby, I will come as soon as I go."

(End of this chapter)