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

The problem of n-s equation describes the dynamics of incompressible fluids, which involves the existence and smoothness of solutions to n-s equations of incompressible viscous fluids.

The n-s equation project team has completed the previous discussion, and now it is only one last step away from finding the complete solution to the existence and smoothness of the n-s equation solution of the incompressible viscous fluid.

Shen Qi believes that among the four key equations, formula (1) is the most important key, so Zhou Yuan listed it as formula (1) and placed it in the front.

Faced with the n-s equation, the millennium problem that has plagued people for many years, Zhou Yuan was able to do this, reflecting great academic progress and a high level of mathematics.

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

"A little bit, a little bit."

The idea became clearer and clearer, and the disguise of the problem was stripped off layer by layer by layer by layer by layer by layer, and the last veil was wrapped on the final answer, uncovering it and cracking it.

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

After several years of brewing, continuous discussions over the past year, specific implementation, the focus on fire in the past month, the n-s 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 of Hilbert space f(t,x)=(f1(t,x),f2(t,x),f3(t,x))∈r^3. He worked hard to calculate the scalar product of Euclidean space and the most important norm.

The last veil of mystery of n-s equation was unveiled tonight, in Shen Qi's study.

Shen Qi wrote an equation on paper, which is the last equation of the entire project. Compared with the long and long system of partial differential equations in the previous article, the final conclusion is not too complicated:

Σ(iiuk(t,)ii^2l2(Ω)+∫iigraduk(η,)ii^2l2(q)dη)≤Σ∫iifk(η,)ii^2l2(q)dη

"Yes, this is the general solution of the n-s equation with universal significance. I finally found you!" Shen Qi clenched his fists and waved it twice. He rushed out of the study, wanting to kiss his daughter and wife.

"Forget it, let's kiss you again at dawn." Shen Qi saw the wall clock on the wall. It was 2 a.m., and his wife and daughter were already asleep.

Shen Qi returned to the study and verified it. This general solution satisfies equations (1)-(4), and it is the undoubtedly correct answer.

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

"You stayed up all night?" Ou Ye got up, but the baby had not woken up yet.

"The n-s equation has been completed, and there are not many projects that can keep me up late in the future." Shen Qi sat on the dining table and had breakfast with Ou Ye.

"It's done, it's great, let's take a look." Ou Ye was very excited. She breastfeeds every day and was in confinement at home. She was actually boring after being a nurse for a long time.

Although the professionalism is not appropriate, the solution to the n-s equation is also equivalent to a dose of stimulant for Ou Ye.

Shen Qi presented the manuscript of the n-s equation to his wife: "I have sorted it out, but it is still a bit messy. This is the first edition. Please read it by Dr. Ou and correct it."

Without looking at the extremely complex derivation calculations and discussions in the previous article, Ou Ye turned directly to the conclusion page behind, staring at the general solution of the n-s equation, and without smashing his eyes: "That's it?"

"Yes, that's all." Shen Qi nodded and took a cup of coffee to refresh himself.

In a short period of time, Ou Ye couldn't understand Shen Qi's manuscript thoroughly. Her intuition told her that her husband had done another super awesome thing: "Congratulations to your husband, but you still have to be careful and don't stay up late."

"My wife is the best." Shen Qi kissed Ou Ye, and suddenly came to a whim and pulled out the last page of the manuscript, which was the page with the general solution of the n-s equation, and took a pen to write on the paper: My beloved daughter Chen Nofi for 64 days, her father broke the Navi Stokes equation, and her mother passed the test.

"You are here to remember!" Ou Ye laughed and said, "Nofi's mother laughed but didn't say anything because she was not professionally good. She just made a soybean."

Shen Qi handed the manuscript to Ou Ye: "The last page is the most important conclusion page. This page of manuscript is the first version of the manuscript I wrote when I was the most courageous. Please save this page for Nofi's mother and hand it over to Nofi in the future and pass it on from generation to generation."

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

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

When he arrived at the center, Shen Qi rewrites the last page, scans more than 200 pages of manuscripts into PDF format, and then convenes Weiteng, Zhou Yu'an and Xiao Junlong for a meeting.

"I have calculated the general solution. Next, please ask the three to verify it separately and wait for your news." Shen Qi, who had been in a night, forced himself to refresh himself by caffeine. He looked energetic, but in fact he was very tired.

"The boss is indeed the boss!" Xiao Junlong jumped up excitedly, Weiteng and Zhou Yuan were also excited.

Weiteng and the other three each found a quiet and independent space to verify the solution to the n-s equation.

Shen Qi was at the center and woke up and was resurrected with full blood.

Manual verification cannot be completed in one or two days. While manual verification, Shen Qi began to contact Yanda Supercomputing Center to make an appointment for the use of Shenteng x8810.

The Shenteng series supercomputer was developed and manufactured by the same Chinese company. Yanda purchased the latest supercomputer Shenteng x8810 a few years ago, named "Weiming No. 1". After several years of operation and exploration, "Weiming No. 1" has become mature and stable, ranking within the top 20 global supercomputer.

Manual verification mainly involves forward and reverse derivation, verification, massive data processing and prediction from logical ideas. No human can handle it, and Shen Qi cannot handle it, so he must use supercomputers.

The director of Yanda Supercomputing Center heard that Shen Qi wanted to use "Weiming No. 1" to verify the n-s equation, and he absolutely supported it and reserved time for Shen Qi to use.

Weiteng, Zhou Yu'an and Xiao Junlong are very familiar with this set of n-s equation cracking solutions, and many of the work was done by them.

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

"Wow, perfect, Qi, it seems that we have really solved the n-s equation, at least there is no logical problem." Weiteng and Shen Qi shook hands and hugged, and the two Philippine award winners joined forces to complete a topic.

A few days later, Zhou Yu'an and Xiao Junlong completed the manual verification. No problem, let's go to the supercomputer!

Yanda Supercomputing Center welcomes the n-s equation project team led by Shen Qi and Weiteng.

"Weiming No. 1" has been launched. The researchers at Yanda Supercomputing Center are ready to make all preparations and wait for Professor Chen to start the calculation program.
Chapter completed!