Chapter 356 The general solution of the NS equation!
Chapter 356 General solution of NS equation!
Lin's curvature tensor can be used to describe many states of fluids. It can be used to describe a shape of a manifold in differential form.
The so-called manifold can be directly regarded as a fluid or a curved plane. For example, if a very smooth steel plate is bent, its surface will form a manifold.
Like the Riemannian curvature tensor, it can be used to express the standard square of the curvature of the Riemannian manifold.
The Lin's curvature tensor developed by Lin Xiao describes another kind of manifold, which shows that it is not necessarily smooth, because this manifold may not even be a curved surface, but may 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 describe fluids perfectly!
Seeing this, Lin Xiao pursed her lips and smiled slightly.
"Then, based on Lin's curvature tensor, the vortex state fluid in the original magnetic fluid thruster can be described like this..."
『ρdv/dt=pF+▽·p』
『ρ=-pl+2μ(s+l▽·u/3)+……』
Although Lin Xiao has not directly found the general solution to the NS equation, he is trying to solve this problem in a special to general way.
From the specific to the general, it 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 if we can solve the NS equation from the specific to the general, it will be relatively more convenient.
Of course, in the past, there was no such special fluid case that could directly allow mathematicians to make the leap from the special to the general.
Coincidentally, Lin Xiao happened to join Ma Weimin's project, and then happened to discover the vortex flow in the magnetic fluid thruster, which could help him achieve such a leap from the general to the special.
As a result, Lin Xiao continued to achieve breakthroughs in the NS equation like an overwhelming force.
However, as he discovered before, due to the huge amount of calculations brought by his Lin's curvature tensor, his unstoppable success took almost a month.
…
The time has entered mid-July.
In Lin Xiao's office at Beijing University.
[So, according to Equation 1, Equation 5, Equation 11, Equation 30... we can get:]
[NS equation: V/t+(V·▽)V=f-1/ρ……]
[Write its characteristic equation...]
[Substituting equation 31 into the original equation, the solution is b=1/2]
[So, we can find the general solution of the NS equation as ρ=Vuvw+ρG+...]
[Substituting this general solution into equation 3 for verification, it is obvious that we can see that both sides of the equation are equal]
[Therefore, it can be proved that Equation 32 is the general solution of Navier-Stokes equations. 】
[Therefore 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 to the NS equation. 】
[So, the NS equation has a solution and is smooth. 】
【Certificate completed.】
After writing the last two words stroke by stroke, Lin Xiao picked up the pen cap next to him and inserted the gel pen with the ink that was about to bottom out back into the pen cap like a knife being sheathed.
"Finally, it's done."
Lin Xiao rubbed his sore wrist.
For almost a month, he had been carrying out extremely complex calculations, and every day his mind seemed to be operating at full capacity.
If his brain's maximum tolerable development hadn't reached 120% of its original capacity, he would probably have to wait a while to get it done.
Then, looking at the general explanation full of mathematical beauty, Lin Xiao's face also showed a smile that saw the truth.
The undulating waves follow the boats that are meandering through the lake, the turbulent airflow follows the flight of our modern jet aircraft, and the invisible water currents sway beside the deep-sea submarine.
Mathematicians and physicists are convinced that both breezes and turbulence can be explained and predicted by understanding the solutions to the Navier-Stokes equations.
However, this equation, written down in the 19th century, has stumped mathematicians and physicists who regard it as the Bible for nearly two hundred years.
But finally, until today, it has been truly and completely solved.
As a mathematician and physicist, Lin Xiao is undoubtedly the happiest scientist in the world at this moment.
At this time, the sound from the harvest also sounded.
System: "Congratulations to the host for proving the existence and smoothness of the solution to the Navier-Stokes equation, and completing its solution. The mystery of fluids has been completely solved in your brain, and the truth is a little closer to you.
From now on, you will become the master of fluids."
"This reward is 15,000 mathematical experience points, 15,000 physical experience points, 150 truth points, [Pneumatic Diagram]."
Hearing such a luxurious reward, Lin Xiao's face suddenly showed an expression of excitement.
Good guy, the two doors add up to a total of 3 W experience, not to mention 150 truth points. This makes his current truth points officially break through the thousand mark, reaching 1062.5.
However, the aerodynamic diagram that was also awarded made Lin Xiao couldn't help but wonder, what is this thing?
However, just when he was about to take a look, there was suddenly a violent knock on the door.
He was stunned for a moment, then said: "Please come in."
Then, he saw a group of professors from the School of Mathematics walking in.
The first ones were Xu Ji and their dean Zhao Qi.
Seeing this formation, Lin Xiao couldn't help but ask: "What is this, everyone?"
Zhao Qi said with a smile: "Academician Lin, congratulations, our School of Mathematical Sciences has added another academician!"
Xu Jiye said: "You boy, you suddenly entered the list of academicians without any notice. You are amazing! Your teacher and I have only been academicians for a few years."
Lin Xiao showed a confused expression: "What? Academician?"
"Why, you don't know yet?"
Everyone else was stunned when they saw Lin Xiao's appearance.
Shouldn't Lin Xiao be the first to know?
At this moment, Lin Xiao's cell phone suddenly rang.
When he saw it, it was Ma Gaoliang. When he looked at the crowd in front of him, he suddenly had a guess.
After answering the phone, Ma Gaoliang on the other 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 stunned for a moment, and then he realized what was going on. He knew the reason, and then he smiled and said, "Oh, I know why you don't know. Let me tell you. The official announcement of this year's announcement was just made.
Among the new academician candidates, your name is among them."
"Moreover, you are an academician of the Academy of Sciences and the Academy of Engineering. Professor Lin, congratulations."
Lin Xiao was suddenly surprised: "What? Academicians 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 that's no problem." Lin Xiao finally came to his senses and responded.
"Haha, I won't bother you anymore. 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.
Did you become an academician just like that?
Is this a little too sudden?
Think about it, he is only 23 years old.
But then he remembered what the old man had asked him: "Do you want to be an academician?"
Okay, that’s it straight away.
And he is also an academician of both academies.
So far, how many people in China have served as academicians of both academies?
Isn't this some kind of imperial decree...cough cough.
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 all looked at Lin Xiao with smiles. After all, the phone call Lin Xiao just answered obviously showed that he already knew that he had become an academician.
"Academician Lin, how are you?" Xu Ji said with a smile.
Seeing this young man, who was his student at first, turned into an academician in the blink of an eye, Xu Ji was not only happy but also filled with emotion. A genius is a genius everywhere.
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, everyone else laughed.
"Okay! Then we will wait for Academician Lin's first celebration banquet."
"Then we won't disturb Academician Lin."
As they talked, the group of people left.
Seeing this, Lin Xiao laughed and shook his head.
At this time, he saw three figures sneaking in, and they were clearly his three students.
"Professor...ah, no, academician, we..."
Lin Xiao smiled and cursed: "Don't pretend to be pitiful here, you can just go together when the time comes."
"Okay! Long live the professor!" Zhao Guodong shouted immediately.
Li Min next to him slapped him and said, "I told you to call me academician!"
Lin Xiao saw the three of them excited, as if they had become academicians.
He waved his hand and said, "Okay, don't stay here anymore, go do your own things."
"Okay, Mr. Academician, you are busy!"
The three people 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, and after a moment of excitement, he accepted the addition of "academician" to his name.
Then he looked back at the general solution to the NS equation that he had solved.
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 value of the simple millennium problem is relatively low.
So he can publish the proof process of the NS equation in the Millennium Problem.
As for the general explanation, let them study it themselves first.
