From Almighty Scholar to Chief Scientist

Chapter 356 General Solution of NS Equation!

Lin's curvature tensor can be used to describe many states of fluid, and it can be used to describe a form of manifold in differential form.

The so-called manifold can be directly regarded as a fluid, or a curved plane, such as bending a very smooth steel plate, and its surface forms a manifold.

Like the Riemannian curvature tensor, it can be used to express the standard square of the Riemannian manifold curvature.

The Lin’s curvature tensor developed by Lin Xiao describes another manifold, which is not necessarily smooth, because this manifold may not even be a curved surface, but have angles.

In this way, this manifold can be completely named after Lin Xiao, that is, Lin's manifold.

And with these two, Lin Xiao will be able to perfectly describe the fluid!
Seeing this, Lin Xiao pursed his lips and smiled slightly.

"Then, based on Lin's curvature tensor, the fluid in the vortex state in the original magnetic fluid thruster can be described in this way..."

"ρdv/dt=pF+▽·p"

『ρ=-pl+2μ(s+l▽·u/3)+……』

Although Lin Xiao does not directly seek the general solution of the NS equation, he tries to solve this problem from special to general.

From special to general is also an important method to solve problems, and it is very meaningful for solving NS equations.

After all, it is very difficult to directly solve the general solution of the NS equation.

Even Lin Xiao had to admit this.

And it will be much more convenient if we can solve the NS equation from special to general.

Of course, in the past, there was no such a special fluid case that could directly allow mathematicians to realize the leap from special to general.

Coincidentally, Lin Xiao happened to join Ma Weimin's project, and then happened to discover the eddy current in the magnetic fluid thruster, which could help him achieve such a general to special leap.

So the following Lin Xiao continued to achieve breakthroughs in the NS equation as if the momentum was breaking through.

However, as he discovered before, due to the huge amount of calculations brought about by his Lin's curvature tensor, his momentum has been broken for nearly a month.

……

Time has entered mid-July.

Shangjing University, in Lin Xiao's office.

[So, according to formula 1, formula 5, formula 11, formula 30... we can get:]

【NS equation: V/t+(V·▽)V=f-1/ρ...】

[Write down its characteristic equation...]

[Substitute Equation 31 into the original equation to get b=1/2]

[So, we can find the general solution of the NS equation as ρ=Vuvw+ρG+...]

[Substitute this general solution into Equation 3 for inspection, and we can see that both sides of the equation are equal]

[Therefore, it can be proved that formula 32 is the general solution of Navier-Stokes equations. 】

[So we can prove the existence of solutions to the NS equation. 】

[And we can easily find that the general solution has smoothness, so we can prove the smoothness of the solution of the NS equation. 】

[Therefore, the NS equation has a solution and has smoothness. 】

[The certificate is completed. 】

After writing the last two characters stroke by stroke, Lin Xiao picked up the cap next to it, and inserted the gel pen whose ink was about to run out back into the cap as if sheathing a knife.

"Finally finished."

Lin Xiao rubbed his sore wrist.

For almost a month, he has been doing extremely complicated calculations, and his mind seems to be operating at full capacity every day.

If it wasn't for the fact that his brain's maximum development rate had reached 120% of the original level, otherwise he might have to wait for a while to get it done.

Then, looking at the general solution full of mathematical beauty, Lin Xiao also had a smile that could see the truth on his face.

Undulating waves follow the boats meandering through the lake, turbulent air currents follow the flight of our modern jet aircraft, and invisible currents sway beside the bathyscaphe.

Mathematicians and physicists are convinced that both breezes and turbulent flows can be explained and predicted by understanding the solutions to the Navier-Stokes equations.

Yet the equation, written in the 19th century, baffled mathematicians and physicists who regarded it as a bible for nearly 200 years.

But finally, until today, it's really been sorted out.

Lin Xiao, who is a mathematician and physicist, is undoubtedly the happiest scientist in the world at this moment.

At this time, the voice from Harvest also sounded.

System: "Congratulations to the host for proving the existence and smoothness of the solution of the Navier-Stokes equation, and completing the solution. The mystery of the fluid has been completely unraveled in your brain, and the truth is a little closer to you. From now on, you will be the master of the fluid."

"This time we will reward 15000 math experience points, 15000 physics experience points, 150 truth points, [pneumatic illustration]."

Hearing such a luxurious reward, Lin Xiao's face suddenly revealed an expression of excitement.

Good guy, the total of 3 W experience in the two disciplines, not to mention 150 truth points, which makes his current truth point officially break through the 1062.5 mark and come to [-].

However, Lin Xiao couldn't help but feel puzzled by the pneumatic diagram that was rewarded, what is this thing?

However, just as he was about to take a look, there was a sudden loud knock on the door.

He froze for a moment, then said, "Please come in."

Then, he saw a group of professors and teachers from the School of Mathematics walking in.

The first ones are Xu Ji and their dean Zhao Qi.

Seeing this battle, Lin Xiao couldn't help but ask, "Where is this, everyone?"

Zhao Qi said with a smile: "Academician Lin, congratulations, our School of Mathematical Sciences has added another academician!"

Xu Ji also said: "Boy, you suddenly entered the list of academicians without making a sound. You are amazing! Your teacher and I haven't been an academician for a few years."

And Lin Xiao showed a blank expression: "What? Academician?"

"Why, you don't even know?"

The others were taken aback when they saw Lin Xiao's appearance.

Shouldn't Lin Xiao know about it first?

And at this moment, Lin Xiao's cell phone rang suddenly.

He saw that it was Ma Gaoliang, and when he looked at the crowd in front of him, he suddenly had a guess.

After answering the phone, Ma Gaoliang, who was on the opposite side, came up and said with a smile: "Professor Lin Xiao, congratulations, you have become our academician this year."

Lin Xiao immediately said: "Director Ma, don't tell me anything else, first tell me what's going on, why did I suddenly become an academician?"

"You don't know yet?" Ma Gaoliang was taken aback for a moment, then he realized the reason, and then smiled and said: "Oh, I know why you don't know, let me tell you, just now the official announcement of this year's Among the newly added academician candidates, your name is among them."

"And, you are an academician of the Academy of Sciences and the Academy of Engineering, Professor Lin, congratulations."

Lin Xiao suddenly became surprised: "What? Academician of the two academies?"

"Yes, haha, I'm just waiting for you to treat me to dinner, Academician Lin." Ma Gaoliang said with a smile.

"Uh...of course it's okay." Lin Xiao finally came back to his senses and responded.

"Haha, then I won't bother you, I have something to do, so that's it." Ma Gaoliang said with a smile, and then hung up the phone.

"Ok."

Lin Xiao responded, and then put down the phone.

At this time, he still couldn't believe it.

Become an academician just like that?

Is this a little too sudden?
Come to think of it, he's only 23 years old this year.

But at this time, he remembered what the old man asked him: "Do you want to be an academician?"

Well, that's it for now.

And he is also an academician of the two academies.

How many people in Huaguo are academicians of the two academies at the same time?

Is this a kind of imperial order... Ahem.

At this time, he suddenly remembered that there were many people in front of him.

So he raised his head and looked at Xu Ji and the others again.

At this time, these people also looked at Lin Xiao with a smile on their faces. After all, the phone call that Lin Xiao connected just now clearly showed that he already knew that he had become an academician.

"Academician Lin, how are you doing?" Xu Ji said with a smile.

Seeing this young man, who was his student at the beginning, turned into an academician in the blink of an eye, Xu Ji was relieved and also filled with emotion. A genius is a genius everywhere.

And Lin Xiao looked at so many people, waved his hands, and said with a smile: "A treat, definitely a treat."

Hearing Lin Xiao's words, the others all laughed.

"Okay! Then we can wait for Academician Lin's first celebration dinner."

"Then let's not disturb Academician Lin."

While talking, this group of people also left.

Seeing this, Lin Xiao smiled and shook his head.

And at this time, he saw three figures sneaking in, they were his three students.

"Professor...ah no, Academician, that us..."

Lin Xiao scolded with a smile: "Don't pretend to be pitiful here, just go with you when the time comes."

"Okay! Long live the professor!" Zhao Guodong shouted immediately.

Li Min, who was next to him, slapped him and said, "I've said it all, I want to call you an academician!"

Lin Xiao looked at the excitement of the three of them, as if they had become academicians.

He waved his hand and said, "Okay, don't stay here with me, go do your own things."

"Alright, Academician, you are busy!"

The three of them immediately bowed to Lin Xiao, and then quickly slipped away.

As the door closed, the office finally returned to calm.

Lin Xiao returned to his seat, his heart was also surging for a moment, and he accepted the addition of "academician" to his name.

Then he looked back at the general solution of the NS equation that he had worked out.

Now, he needs to deal with this proof process and hide the general solution, leaving only the existence and smoothness of the solution.

The general solution has strategic significance, but the pure millennium problem has relatively low value.

So he can publish the proof process of the NS equation in the Millennium Problem.

As for the general solution, let them do their own research first.

(End of this chapter)