Chapter 412 Explosion Equation?

Regarding the idea of ​​proof, Lu Zhou and Professor Fefferman reached a consensus, but how to construct this abstract bilinear operator B' has become a very serious problem.

It must have a similar nonlinear structure to Euler's linear operator B in μ(t), but at the same time it differs from B.

In partial differential equations, "nonlinear" means complex.

The series of problems derived from it are even more complex...

At the first seminar in March, a small conference room at the Institute for Advanced Study in Princeton.

Looking at the calculation formula on the blackboard, Professor Fefferman said thoughtfully.

"I can assure you that we are very close to the end result, just a little bit closer."

Throwing the chalk stub on the desk, Lu Zhou took two steps back, stared at the blackboard, and nodded.

However, even though he was nodding, his face was not full of joy, instead his expression was solemn because of the expression in front of him.

After a while, Lu Zhou said.

"...I feel the same way."

Professor Fefferman sighed and lowered his arms.

"Sometimes the distance between failure and success is only a little bit, you know? I'm even starting to doubt now..."

Lu Zhou cast him a questioning look.

"Suspect?"

Professor Fefferman nodded: "Although we were initially optimistic that the proposition must be correct, more and more results tell us that it may not be as perfect as we imagined."

When he said this, Professor Fefferman's tone was full of uncertainty, and he didn't have the calm casualness when facing students in class.

After so many years, this is the first time he has shown such an uncertain expression on the calculation formula he wrote down.

Staring at the blackboard solemnly, Lu Zhou was silent for a while before opening his mouth with difficulty.

"This is ridiculous."

Professor Fefferman sighed: "Yes, this is ridiculous, but...it is not without reason."

As he spoke, he took out a cigarette and a lighter from his pocket.

In principle, smoking is not allowed in meeting rooms, and smokers must go to designated smoking rooms.

But if it is for research, you can ignore this rule.

After all, this Institute for Advanced Study was established for science, and all the rules here are to serve science and make it easier for scholars to study science.

Without any hesitation, Professor Fefferman lit the cigarette, and carefully placed it on the multimedia desk.

Ethereal smoke spirals upward.

After a short period of entanglement and entanglement, the gradually enlarged smoke column finally dispersed in the air without leaving a trace.

Staring at this natural phenomenon, Professor Fefferman said in a soliloquy voice as if to convince himself.

"The final destination of all systems that can be predicted is chaos, just like our equation. The μΔ value that explodes with the time item fits the truth of the universe in a sense. When the time variable is amplified, we will explode at some unknown singularity, where it will no longer be smooth..."

This particular point is not infinite, but it seems to exist.

It is difficult to solve its value with the existing mathematical methods, just as mathematicians are unable to solve the NS equation. However, through the method of indirect proof, it can be proved that it does exist...if the proof process is correct.

Having said that, Professor Fefferman stopped talking, but silently smoked cigarettes, one after another.

Lu Zhou can be sure that this is definitely not for science, but just a way to vent his restlessness.

He admitted that this was an unacceptable thing to do.

The results of the calculations are obvious, but they deviate from the well-known common sense.

Will a car on the highway disintegrate at a certain point in time without warning? This is obviously impossible, even in the worst worst case, it is just a ticket from the traffic police.

If their conclusion is correct, then the NS equation in three dimensions will undoubtedly "explode" at a certain point.

And this also means that at this point in time or space, it may no longer have regularity...

This is ridiculous!

...

The study of NS equations has fallen into an unexpected bottleneck.

In the evening, Lu Zhou resumed his previous life rhythm, changed into sportswear, and jogged along Carnegie Lake, trying to relax by breathing fresh air.

Unfortunately, he didn't get his wish.

The question discussed with Professor Fefferman in the afternoon still lingers in his mind.

The running speed became faster and faster, and before he knew it, Lu Zhou sprinted.

He didn't stop until he exhausted all his strength and his legs began to feel as heavy as lead.

Panting heavily, Lu Zhou walked to the lawn by the lake, and sat on the ground with some exhaustion.

At this moment, a can of sports drink was thrown from the side, smashed on the soft lawn, and rolled to his hand.

Lu Zhou looked up and saw Molina wearing a tracksuit standing not far away, holding another can of the same drink, and greeted him with her eyes.

"It's for you."

Hearing what she said, Lu Zhou was not polite, opened the can, raised his head and took a sip.

Taking a deep breath, feeling the coldness spread from his chest, he raised his hand and wiped his mouth.

"thanks."

"You're welcome."

Sitting next to her, Molina opened her can of drink and took a sip.

Looking at Lu Zhou who was still breathing unsteadily, she said casually in a chatty tone.

"It's not like you."

Lu Zhou grinned: "Which aspect are you referring to?"

Molina: "Two months ago, your physical strength was much better than now. It seems that this holiday has let you relax."

When she said this, Molina's tone was gloating, although Lu Zhou didn't know what she was gloating about.

No matter how slack he was some time ago, with his current achievements, he can still kill her and her mentor more than twice at the IMU conference in August this year...

"Maybe."

Lu Zhou made a shooting motion and threw the can into the trash can by the lake.

Without any suspense, his shot was impartial and hit the bull's-eye.

However, his sight seemed to be glued to the surface of the lake, and he couldn't move it away.

The silence lasted for about five minutes, and Lu Zhou suddenly said.

"You said this Carnegie Lake, will it suddenly explode?"

"You mean there are bombs buried under the lake?" Molina raised her eyebrows and said teasingly, "In this country, this joke can't be played around."

Lu Zhou smiled, shook his head and said, "I mean, under normal circumstances."

Molina took it for granted, "Of course not...Why do you ask that?"

Lu Zhou sighed: "Because my mathematics is telling me that this possibility does exist."

Molina burst out laughing.

"It's so bizarre."

Staring at the sparkling lake in the setting sun and at the members of the kayak club training on the lake, Lu Zhou said meaningfully.

"Yeah, it's so bizarre."

But, is there such a possibility?

For example, for the water molecules moving randomly in the system, the vector of the motion at a certain moment happens to be outward at the same time? It's like natural volatilization, but because of various coincidences, this "volatility process" is relatively intense, and the energy is released in an instant.

However, no matter how he opened his mind, Lu Zhou couldn't make up the picture of the kayak on the lake being blown away by the instantly evaporated lake water.

unless……

Throw a big bomb in there or something.

However, what he wants to discuss is obviously not this special case of "adding empirical parameters".

Molina asked: "Is the still lake exploding itself part of the NS equation?"

Lu Zhou nodded and said frankly.

"That's right."