Molina stared at Lu Zhou for about half a minute before she suddenly reached out her hand.
Lu Zhou looked at the hand that was touching his forehead and subconsciously dodged it.
"What do you want?"
Molina nonchalantly retracted her hand and said in a serious manner, "Nothing, I just want to see if you have a fever."
Lu Zhou: "…"
Molina looked at Lu Zhou seriously and said, "Honestly, even though I've never studied partial differential equations before, why did you make the problem so complicated?"
Lu Zhou patted the grass off his pants and stood up.
"I want to make it simpler, but I can't help it, it's just that complicated."
Molina also stood up and walked in front of Lu Zhou. "If the result of a calculation violates common sense, then there's a high probability that something is wrong."
Lu Zhou didn't deny her statement.
"Maybe you're right, because I think so too. However, compared to whether the solution of the three-dimensional Navier – Stokes equation has global regularity at a particular point, I want to know why. "
Lu Zhou paused for a second and continued to stare at the lake.
"Why did our equation explode?"
…
"Explosion" was also known as divergence in the field of computational fluid dynamics. Many foreign authors liked to use the word "blow-up" to describe this troublesome phenomenon.
In mathematics, it also referred to a lot of problems. For example, it could be that the denominator of the solution was zero, or that the solution matrix didn't converge …
For the Navier – Stokes equation, the so-called explosion problem, or the divergence problem, referred to a point in time and space where the fluid flowed faster and faster until it reached infinity, which was beyond common sense.
Lions and others proved half a century ago that this point did not exist in the two-dimensional case. This was the uniqueness, regularity, and stability of the overall weak solution of the Navier – Stokes equation in the two-dimensional case. However, the academic community still didn't have a consensus on what the three-dimensional Navier – Stokes equation was like.
The general view of the mathematics community was optimistic about the existence and smoothness of a three-dimensional Navier – Stokes equation solution. People in computational fluid dynamics obviously agreed with this view. Otherwise, wouldn't the phenomenological models they built based on experimental data be equivalent to using lies to explain lies?
Lu Zhou returned home with a body full of sweat. He threw the clothes into the washing machine and turned around to take a shower.
The feeling of hot water flowing down his head calmed him down a lot.
There might be problems with the idea of indirect proof through abstract bilinear operators. Instead of repeatedly struggling with an uncertain problem, it was better to be prepared, such as trying to find an alternative way of thinking.
This was a game that challenged the pinnacle of human intelligence, and there was no way to solve the problem.
Before Calaby's conjecture was solved, the differential geometry community had never thought that partial differential equations and Riemann geometry could be used like this. After Karaby's conjecture was solved, geometric analysis based on the PDE method came into being.
Maybe when he solved the Navier – Stokes equation, he would discover something even greater?
After he went back to his study room, he turned on his computer and began to search for literature on the Navier – Stokes equation.
After all, the Navier – Stokes equation was one of the most important problems in the field of partial differential equations. Therefore, scholars in the field of partial differential equations had produced a lot of beautiful research results on this equation.
Whenever Lu Zhou reached a bottleneck in his research, he would search for the missing piece of the puzzle by searching through his database.
Just like when Perelman saw Hamilton's thesis on understanding the Ricci stream singularity, he immediately used this method to solve the Poincaré conjecture. Lu Zhou was also looking for something similar.
However …
It obviously wasn't easy to find this piece of the puzzle.
The sunset outside the window was already covered with stars. The clock on the wall had passed 12 o 'clock and began to move towards 1 o' clock.
Lu Zhou let out a long sigh and leaned back in his chair. He pinched his temples.
The erratic thoughts in his mind were like solidified ink for a moment, then dispersed into a column of smoke the next moment, giving him a headache.
However, Lu Zhou suddenly had an epiphany.
"If I don't have a tool, why don't I build one myself …"
If every molecule was abstracted into a point, and the collection of these points was abstracted into a space with local Euclidean space properties, he could construct an approximate three-dimensional manifold based on this, and he could apply topology methods to it …
This seemed to make a "simple" problem even more "complicated".
But it seemed like …
It would work?
His eyes became brighter and brighter.
Lu Zhou grabbed a pen and wrote a line of words on a piece of paper.
[Lu Manifold]
Then, the brush in his hand couldn't stop moving …
…
When one was fully immersed in a task, time always passed by quickly.
In the blink of an eye, it was already April.
Over the past month, Lu Zhou, who locked himself in his room, had a short and monotonous spring break.
During this time, other than Vera, who came to his room once and gave him a teaching report, Lu Zhou almost cut off all communication with the outside world.
In fact, even though he was the one who asked Vera to send those things over, he had placed them in the corner of the study room and hadn't touched them at all.
At Princeton, Professor Lu's unique way of researching problems was an interesting story. Even the freshmen had heard about it from the older students.
Perhaps Professor Fefferman knew that Lu Zhou's research had entered a critical period, so he didn't disturb him. Instead, he temporarily stopped the regular communication meetings and began to conduct independent research.
And now, these efforts finally bore fruit.
Lu Zhou put down the pen in his hand and looked at the stack of draft papers in front of him. He smirked.
Lu Zhou's tense mind finally relaxed, and he began to think of some unimportant things.
For example, wouldn't the name Lu Manifold be a bit unpleasant?
Should I change it to LuZ-stream or LuZhu-stream?
After thinking about it, Lu Zhou felt like it was better not to make things difficult for future students.
The former seemed to have strange meanings, and the latter didn't sound good.
"I'll just call it Lu Manifold, and the English translation is L Manifold, or L Stream for short!"
Lu Zhou was a lot more satisfied with this name. He then changed the title of the draft papers and stacked them on the corner of the table. He was going to organize the contents one by one on his computer.
When he turned on his computer and was about to start working, a string of bubbles suddenly popped up on the workbar in the lower right corner of the screen.
Xiao Ai: [Master, you have mail! (?????)??】
When Lu Zhou saw this message, he clicked on the link that Xiao Ai threw at him and logged into his email.
The email was from Annual Mathematics.
As for the content, it was obviously about the proof of the Collatz conjecture.
Lu Zhou read the email from beginning to end, and a smile appeared on his face again.
Although it was expected, after reading the email, he was sincerely happy for his students.
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