Chapter 477 New Development of N-S Equation
Chen Nofi will be full moon tomorrow, and today is exactly the day before the start of primary and secondary schools in the country.
At the request of relevant departments, primary and secondary school students across the country will watch the "School Classroom" program at 8 o'clock tonight.
This year's "School Classroom" is different from previous years. At 8 pm, "School Classroom" will be broadcast on time, without any ads.
The one who warmed up the venue was not the entertainment talent singer with heavy makeup, but the Chinese team at the World College Games men's basketball runner-up.
The young men of the basketball team came from universities across the country. In the just-concluded World College Games men's basketball semi-finals, under the difficult situation of 16 points behind, relying on the tenacious fighting spirit and impeccable team cooperation, they staged a shocking reversal, eliminating the strong team Russia, entering the finals historically, and winning a precious silver medal.
The Chinese college boys' basketball team showed a majestic momentum, demonstrating the masculinity of Chinese youth's passionate and moving the whole of China.
The Chinese college boys' basketball team who returned from honor introduced themselves at the opening of "The Opening Classroom". They were all college students, some of whom studied materials, some of whom studied machinery, and some of whom studied law, and many of them were academic masters.
The program then played a set of VR, which is a wonderful collection of famous Chinese scholars.
Physicists keep breaking the records of quantum entanglement, astronomers create national weapons to explore the universe, writers splash ink and sublimate their souls, and mathematicians are full of energy to solve the problems of the century.
Shen Qi held his daughter and watched "The Opening Classroom" in front of the TV. He was the mathematician in the TV screen.
Receiving patriotic education and starting with children, Shen Qi is very satisfied with this program this year: "That's right, this is the real school start education."
After the show was broadcast, no one complained about it from the country, and they all liked it.
The next day, school started.
Shen Qi held a full moon banquet for his daughter today and invited a few relatives and friends to the banquet.
Zhou Yuan brought a bunch of gifts, including milk powder, baby clothes, dolls, and all kinds of them.
"Nowi's eldest niece, I wish you good health and growth." Zhou Yuan said to Chen Nofi.
Chen Nofi smiled and didn't speak. She was developing faster. She would smile at things she thought were interesting one month old, but she couldn't laugh. It would take about one or two months to laugh.
Xiao Junlong gave a piece of jade and said that it was very good and suitable for girls to wear: "Little Nofi, beautiful jade is matched with beauty."
The one-month-old baby couldn't laugh, but could cry. Chen Nofi cried, and Xiao Junlong scared her like this.
Ou Ye’s best friend Xiao Lian gave him a baby hat.
Chen Nofi smiled again. She would laugh when she saw normal-looking men and women, which was very cute.
Weiteng came to China a few days ago, and this time he returned to the United States for more than two months of rest.
Wei Teng, who followed the local customs, gave a red envelope of 1,000 rmb, which is really a human being.
After holding the full moon banquet, Shen Qi, Wei Teng, Zhou Yu'an and Xiao Junlong came to the center to discuss important matters.
Shen Qi said: "Zhou Yuan has done a pretty job recently. He has proved the corner principle and obtained a set of important data on the n-s equation through the infinite current algorithm of the partial differential equation. Zhou Yuan, please tell me."
Zhou Yuan played the ppt and began to explain: "Based on Professor Weiteng's algorithm framework and Professor Shen's supplementary improvements, I have obtained the following inferences."
Four sets of formulas are displayed on the screen:
(1)?uj/?t+Σuk?uj/?xk=△uj-?p/?xi+fj,(t,x)∈Ω,i=1,2,3; divu=Σ?uk/?xk=0,(t,x)∈Ω
(2)u(t,x)it=0=0
(3)u(t,x)ixk=-π=u(t,x)=π,?u/?xkixk=-π=?u/?xkixk=π,k=1,2,3,0≤t≤a
(4)∫qp(t,x)dx=p0,p0=onst>0
"The problem of n-s equations, we transform into the problem of seeking the velocity vector and scalar function at point x∈Ω and time t∈(0,a)." Zhou Yu'an switched ppt to the next page.
This page writes an inference: "Inference 1: For f∈l2(Ω), if we find the solution of equations (1)-(4), we solve the generalized solution of the n-s equation, and this solution has universal significance."
"Awesome Lao Zhou!" Xiao Junlong stood up after a flash of pain. Zhou Yuan has not been in seclusion in the past few months and has done something amazing.
All the previous derivation and proof work was solved by Zhou Yuan. The only problem and the most critical problem now are to find the solution of formulas (1)-(4) to prove this inference.
"It seems that I'm not doing anything." Wei Teng said with a smile, spreading his hands, and he expressed his affirmation of Zhou Yuan's efforts.
Shen Qi said: "So now we only need to do one thing. Zhou Yu'an just said it very clearly. Prove the inference 1, that is, find the solution of formulas (1)-(4). Then Zhou Yu'an, you should complete this last blow."
"I can't handle it." Zhou Yuan shook his head and looked at Xiao Junlong: "Old Xiao, why don't you get on?"
Xiao Junlong shook his head: "Lao Zhou, you can't handle it, I must not handle it either. The subsequent things are no longer pure mathematics, physics, partial differential equations, and fluid mechanics. They should also be used to deal with it with topology and functional tools. In fact, Lao Zhou, we have outstanding advantages, but we also have common weaknesses, that is, our professional scope is narrow, and comprehensive treatment is still required to handle it."
The n-s equation project has advanced to this stage, and all four people have made contributions.
The current situation is that the two generals Zhou and Xiao have cleaned up all the monsters, and the remaining big boss needs to be solved by two big bosses.
The two big guys looked at each other, okay, let's do it.
The n-s equation project has entered the critical stage, and Shen Qi and Weiteng have divided the labor.
Weiteng has a clear idea and a good overall view, but after all, he is old and it is a bit difficult for him to calculate the high-intensity specificity.
Shen Qi personally handled the cumbersome and complex derivation calculations in the key stage, and Weiteng was responsible for verifying the calculation, finding faults, and finding loopholes.
After the expansion of equations (1)-(4), a large number of partial differential and ordinary differential equation systems are derived, as well as more than a dozen definitions and lemmas that need to be proved.
In order to simplify computing, Shen Qi specially invented a new tool and discussed it with Weiteng.
"From Lemma 2 to Lemma 9, the normal idea is to consider the situation of u2, u3 to infinite, then we need to use Lemma 3 infinity times. The most troublesome thing is the non-negative monotonic increase function, which means that our workload will increase by more than a hundred times."
"So I invented this new tool, which is considered a processing method. It is valid, simple and efficient." Shen Qi showed Weiteng the new method he invented, assuming that pn is the n-dimensional orthogonal projection operator in h, then for any x∈h, when n→∞, pnx→x.
After Weiteng 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, this work continued throughout September, and Shen Qi did not calculate the generalized solution to the n-s equation.
Regardless of whether the n-s equation can be solved or not, Shen Qi gets off work at 5 o'clock every day and goes home on time.
Today, when Shen Qi was teasing his two-month-old daughter, his daughter smiled.
"Nofi, I know it's useless for you to laugh at me. I can't even solve the n-s equation. Let's do this. I can't solve this equation for now. I'll leave it to you when you grow up. OK?" Shen Qi touched his daughter's pink face.
The daughter continued to laugh, drooling.
Shen Qi: "Daughter, then give me some tips?"
Chen Nofi: "Geeh."
Shen Qi was quite surprised: "Nofi laughed out loud, and she burst out laughing in two months!"
Looking at Shen Qi's appearance, Chen Nofi kept laughing. This was a baby girl who loved to laugh: "A little bit."
"A little bit, periodic boundary?" Shen Qi suddenly realized that his daughter said periodic boundary, and that was definitely correct!
Shen Qi handed his daughter to Ou Ye: "The child's mother, hold the baby, I'll come when I go."
Chapter completed!