I just want to be a quiet scholar

Chapter 477

Shen Qi came to the study room, spread out the scroll, and began to deduce and calculate.

The problem of NS equations is the problem of describing the dynamics of incompressible fluids, which involves the existence and smoothness of solutions of NS equations for incompressible viscous fluids.

The NS equation project team has completed the previous discussion, and now it is only the last step to find the complete solution of the existence and smoothness of the NS equation solution for incompressible viscous fluids.

Shen Qi believed that among the four key formulas, formula (1) was the most important key, so Zhou Yuan listed it as formula (1) and put it at the top.

In the face of the millennium puzzle NS equation that has plagued people for many years, Zhou Yu'an's ability to achieve this step reflects his great academic progress and high level of mathematics.

The last blow was handed over to Shen Qi, who made a new calculation, adding boundary conditions to formula (1), that is, giving periodic boundary conditions and initial conditions for spatial coordinates.

"A little bit, a little bit."

The train of thought became clearer and clearer, Shen Qi peeled off the camouflage of the problem layer by layer, and the last layer of veil was wrapped on the final answer, uncovering it and deciphering it.

After improvement by Shen Qi, formulas (1) to (3) have determined the initial conditions and boundary conditions, and the only thing that cannot be determined is the pressure p(t, x).

Several years of brewing, one year of continuous discussion and specific implementation, and the last month of concentrated fire to tackle tough problems, the NS equation project has advanced to this moment, and the pressure cannot stop Shen Qi from moving forward.

Shen Qi obtained a set of vector functions f(t, x) = (f1(t, x), f2(t, x), f3(t, x)) ∈ R^3 in Hilbert space, and he worked hard, Calculated the scalar product of Euclidean space, and the most important norm.

The last layer of mystery of the NS equation was unveiled tonight, in Shen Qi's study.

Shen Qi wrote a formula on paper, which is the last formula of the whole project. Compared with the previous long and cumbersome partial differential equations, the final conclusion is not too complicated:

Σ（∣∣uk（t，）∣∣^2L2（Ω）+∫∣∣graduk（η，）∣∣^2L2（Q）dη）≤Σ∫∣∣fk（η，）∣∣^2L2（Q）dη
"Yes, this is the universal solution of the NS equation. I finally found you!" Shen Qi clenched his fist and waved it twice. He rushed out of the study, wanting to kiss his daughter and wife.

"Forget it, let's kiss again at dawn." Shen Qi saw the wall clock on the wall, it was 2 o'clock in the morning, and his wife and daughter had already fallen asleep.

Shen Qi went back to the study and verified it again. This general solution satisfies formulas (1)-(4), and it is the correct answer without a doubt.

After Shen Qi sorted out the manuscript, the sun rose.

"You stayed up all night?" Ouye got up, but the baby was still awake.

"The NS equation is settled, and there are not many projects that will keep me up late in the future." Shen Qi sat at the dining table and had breakfast with Ouye.

"It's done, that's great, let me have a look." Ouye was very excited, she was breastfeeding every day, confinement at home, being a nanny for a long time was actually boring.

Although the major is not right, the solution of the NS equation is also equivalent to a dose of stimulant for Ouye.

Shen Qi presented the manuscript of the NS equation to his wife: "I've sorted it out, but it's still a bit messy. This is the first edition. Please review it and correct it, Dr. Ou."

Ouye didn't look at the incomparably complicated derivation, calculation and discussion, she directly turned to the conclusion page at the back, staring at the general solution of the NS equation without blinking her eyes: "That's it?"

"Yes, that's it." Shen Qi nodded, drinking a cup of coffee to refresh himself.

It was difficult for Ouye to understand Shen Qi's manuscript in a short period of time. Her intuition told her that her husband had done another super awesome thing: "Congratulations to your husband, but you still have to pay attention to your health and don't stay up late."

"My wife is the best." Shen Qi kissed Ouye, and suddenly, on a whim, he took out the last page of the manuscript, which is the page where the general solution of the NS equation was written, and wrote on the paper with a pen: Beloved daughter Shen Nuofei 64 Today, his father broke the Navier-Stokes equation, and his mother passed the test for the first time.

"You keep a souvenir!" Ouye burst out laughing, and said, "Nuo Fei's mother didn't speak well because of her profession, so she smiled and said nothing, so she was soy sauce."

Shen Qi handed the manuscript to Ouye: "The last page is the most important conclusion page. This manuscript is the first version of the manuscript I wrote when I was in the most courageous state. Please Nuofi's mother keep this page and hand it over to Nuofi in the future. , passed down from generation to generation."

Ouye took the manuscript: "I'll ask Sister Cuiping to take it out and frame it later."

Shen Qi hugged his wife and laughed loudly: "It's so good!"

When he came to the center, Shen Qi rewrote the last page, scanned the more than 200-page manuscript into PDF format, and then called Wei Teng, Zhou Yu'an, and Xiao Junlong for a meeting.

"I've figured out the general solution. Next, please verify the three separately, and wait for your news." Shen Qi, who had been up all night, forcibly refreshed himself with caffeine. He looked energized, but in fact he was already very tired.

"Boss is indeed a big boss!" Xiao Junlong jumped up excitedly, Wei Teng and Zhou Yu'an were also excited.

Each of the three, including Wei Teng, found a quiet and independent space to verify the solution to the NS equation.

Shen Qi catches up on his sleep at the center, and when he wakes up, he comes back to life full of blood.

Manual verification cannot be done in a day or two. While doing manual verification, Shen Qi began to contact Yanda Supercomputing Center to make an appointment to use Shenteng X8810.

The Shenteng series of supercomputers are developed and manufactured by the same Chinese company. Yanda purchased the latest supercomputer Shenteng X8810 a few years ago and named it "Wei Ming No. 20". After several years of operation and exploration, "Wei Ming No. [-]" "Number" tends to be mature and stable, ranking among the top [-] supercomputers in the world.

Manual verification is mainly to carry out forward and reverse derivation and verification from logical thinking, massive data processing and prediction, no one human being can handle it, and Shen Qi can't handle it either, so supercomputers must be used.

The director of Yanda Supercomputing Center heard that Shen Qi wanted to use "Wei Ming No. [-]" to verify the NS equation, he absolutely supported it, and reserved time for Shen Qi to use it.

Wei Teng, Zhou Yu'an, and Xiao Junlong are very familiar with this NS equation solution solution, and they have completed a lot of work.

Even so, it took more than a week for Weiteng, which was the first to complete manual verification.

"Wow, perfect, Qi, it seems that we have really solved the NS equation, at least there is no problem in logic." Wei Teng and Shen Qi shook hands and hugged, and the two Philippine Award winners jointly completed a project.

After a few days, Zhou Yu'an and Xiao Junlong completed the manual verification, no problem, let's go to Super Calculator!
Yanda Supercomputing Center welcomed the NS equation project team led by Shen Qi and Wei Teng.

The "Unnamed No. [-]" has been launched, and the researchers at Yanda Supercomputing Center are gearing up and making all preparations, waiting for Professor Shen's order to start the calculation program.

(End of this chapter)