Shen Qi came to the study, spread out the paper scroll, and began to derive the calculation.

The problem of the N-S equation is a problem that describes the dynamics of incompressible fluids, and this problem involves the existence and smoothness of the solution of the N-S equation of an incompressible viscous fluid.

The N-S equation project group has completed the previous discussion, and now only one last step is to find the complete solution of the existence and smoothness of the N-S equation solution for incompressible viscous fluids.

Shen Qi believes that among the four key formulas, formula (1) is the most important key, so Zhou Yu'an listed it as formula (1) and put it first.

In the face of the millennial problem N-S equation, which has plagued people for many years, Zhou Yu'an was able to do this step, reflecting great academic progress and a high level of mathematics.

The final blow was in the hands of Shen Qi, who made a new calculation to supplement the boundary conditions for Eq. (1), that is, to give periodic boundary conditions and initial conditions for spatial coordinates.

"A little, a little bit. ”

The idea is getting clearer and clearer, and the camouflage of the problem is peeled off layer by layer by Shen Qi, and the last veil is wrapped around the final answer, uncovering it and cracking it.

After Shen Qi's refinement, equations (1) to (3) determine the initial conditions and boundary conditions, and the only one that cannot be determined is the pressure p(t,x).

After several years of brewing, continuous discussion and specific implementation over the past year, and the recent month's gathering of fire, the N-S equation project has advanced to this moment, and the pressure cannot stop Shen Qi's progress.

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

The last layer of mystery of the N-S 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, and the final conclusion is not too complicated compared to the previous long system of partial differential equations:

Σ（∣∣uk（t，•）∣∣^2L2（Ω）+∫∣∣graduk（η，•）∣∣^2L2（Q）dη）≤Σ∫∣∣fk（η，•）∣∣^2L2（Q）dη

"Yes, this is the universal solution of the N-S equation, I finally found you!" Shen Qi clenched his fists and waved twice, he rushed out of the study, wanting to kiss his daughter and wife.

"Forget it, let's kiss it 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 slept.

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

Shen Qi finished sorting out the manuscript, and a round of morning sun rose.

"You stayed up all night?" Ou Ye got up, and the baby hadn't woken up yet.

"Now that the N-S equation is done, there aren't many projects that will keep me up late in the future. Shen Qi sat down at the table and had breakfast with Ou Ye.

"That's it, great, show me. Ou Ye is very excited, she feeds every day, confinement at home, and the wet nurse is actually very boring after a long time.

Although the specialty is not right, the solution of the N-S equation is also equivalent to a dose of stimulant for Ouye.

Shen Qi handed the manuscript of the N-S equation to his wife: "I have sorted it out, but it is still a little messy, this is the first version, please Dr. Ou look at it and correct it." ”

Ou Ye didn't look at the incomparably complex derivation calculations and expositions in front of her, she turned directly to the conclusion page at the back, stared at the general solution of the N-S equation, and didn't smash her eyes: "That's it?"

"yes, that's it. Shen Qi nodded and drank a cup of coffee to refresh himself.

In a short period of time, it was difficult for Ou Ye to read through Shen Qi's manuscript, and 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 body and don't stay up late." ”

"My wife is the best. Shen Qi kissed Ou Ye, and suddenly on a whim, he pulled out the last page of the manuscript, that is, the page with the general solution of the N-S equation, and wrote on the paper with a pen: The beloved daughter Shen Nuofei was 64 days old, her father broke the Navier-Stokes equation, and her mother passed the first test.

"You keep a souvenir!" Ou Ye laughed and said, "Nofei's mother laughed and didn't say anything because of her mismatch, and she made soy sauce." ”

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 at my most courageous, please keep this page for the queen to be handed 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 later." ”

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

Coming to the center, Shen Qi rewrote the last page, scanned more than 200 pages of the manuscript into PDF format, and then called a meeting with Witten, Zhou Yu'an, and Xiao Junlong.

"I've already figured it out, so let's ask the three of you to verify it separately, and wait for your news. Shen Qi, who had stayed up all night, relied on caffeine to forcibly refresh himself, looking energetic, but in fact he was very tired.

"The big guy is really the big guy!" Xiao Junlong jumped up excitedly, and Wei Teng and Zhou Yuan were also excited.

Witten and the other three each found a quiet and independent space to verify the N-S equation solving scheme.

Shen Qi made up for sleep in the center, woke up, and came back to life with full blood.

Manual verification is not something that can be done in a day or two, and at the same time as manual verification, Shen Qi began to contact Yanda Supercomputing Center to make an appointment for the right to use Shenteng X8810.

ShenTeng series supercomputer is 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" tends to mature and stable, ranking in the global supercomputer TOP20.

Manual verification is mainly from the logical idea of forward and reverse derivation, verification, massive data processing and prediction, no human can do it, Shen Qi can't do it, must use supercomputing.

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

Witten, Zhou Yu'an, and Xiao Junlong are very familiar with this N-S equation solving scheme, and a lot of the work is done by them.

Even so, Witten, which was the first to complete manual verification, still took more than a week.

"Wow, perfect, strange, it seems that we really solved the N-S equation, at least logically. Witten and Shen Qi shook hands and embraced, and the two Filipino Award winners teamed up to complete a project.

After a few days, Zhou Yu'an and Xiao Junlong completed the manual verification, no problem, let's go to supercomputing!

Yanda Supercomputing Center ushered in the N-S equation project team led by Shen Qi and Witten.

The "Weiming No. 1" has been launched, and the researchers of the Yanda Supercomputing Center are gearing up to make all preparations, just waiting for Professor Shen to give an order to start the calculation program.