Lu Zhou and Professor Feverman reached a consensus on the idea of proof, 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 is distinguished from B.

In partial differential equations, "nonlinear" means complex.

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

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

Looking at the equation on the blackboard, Professor Feverman said thoughtfully.

"I'm sure we're pretty close to the final result, just a little bit close."

Throwing the chalk head on the lectern, Lu Zhou, who took two steps back, stared at the blackboard and nodded.

However, although he nodded, there was no joy on his face, but because of the calculation in front of him, his face was solemn.

After a long while, Lu Zhou spoke.

“…… I feel that way too. ”

Professor Feverman sighed and lowered his clutched arms.

"Sometimes it's just a little bit of a difference between failure and success, you know? I'm even starting to wonder ......"

Lu Zhou cast an inquiring glance at him.

"Doubtful?"

Professor Feverman nodded: "Although we were initially optimistic that the proposition must be true, more and more results tell us that it may not be as perfect as we think. ”

When he said this, Professor Feverman's tone was full of uncertainty, and there was no trace of the casual calmness that he had with his students in class.

It was the first time in so many years that he had shown such an uncertain expression on the equation he had written.

stared at the blackboard with a solemn face, and was silent for a long time before Lu Zhou spoke with difficulty.

"It's ridiculous."

Professor Feverman sighed, "Yes, that's ridiculous, but ...... It is not without reason. ”

As he spoke, he pulled a cigarette and lighter out of his pocket.

As a general rule, smoking is not allowed in the conference room, and smokers must go to the designated smoking room.

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

After all, this Institute for Advanced Study was built for science, and all the rules here are in the service of science, to make it easier for scholars to study science.

Without hesitation, Professor Feverman lit the cigarette and carefully placed it on the multimedia lectern.

Ethereal smoke spiraled up.

After a short period of entanglement and entanglement, the gradually enlarged column of smoke finally dispersed in the air, leaving no trace.

Staring at this natural phenomenon, Professor Feverman said in a voice like a self-talker, as if trying to convince himself.

"All predictable systems end up in chaos, just like our equations. The μΔ value of the explosion of the time term is, in a sense, exactly in line with the truth of this universe. When the time variable is amplified, our equation will explode at some unknown singularity, and 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 existing mathematical methods, just as mathematicians are at a loss for the solution of the NS equation. However, through indirect proof, it can be proved that it does exist...... If there are no errors in the process.

At this point, Professor Feverman stopped talking, but silently smoked his cigarette, one after the other.

Lu Zhou can be sure that this is definitely not for science, but just a vent to relieve the irritability in his heart.

He admits that this is an unacceptable thing.

The results of the calculations are clear, but they are contrary to common sense.

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

If their conclusion is correct, then there is no doubt that the NS equation in three dimensions will "burst" at some point.

And this means that at this point in time or space, it may no longer be regular......

This is ridiculous!

……

The study of the NS equation has reached an unexpected bottleneck.

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

Unfortunately, he didn't get his way.

The question he had discussed with Professor Feverman that afternoon still lingered in his mind.

The speed of running is getting faster and faster, and before you know it, Lu Zhou is sprinting.

It wasn't until he had exhausted all his strength and his legs began to feel as heavy as lead that he gradually stopped.

Panting, Lu Zhou walked to the lawn by the lake and sat on the ground a little decapitated.

Just then, 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 Mo Lina, who was wearing a sportswear, standing not far away, carrying another can of the same drink in her hand, and greeted him with her eyes.

"Yours."

Hearing what she said, Lu Zhou was not polite, opened the can, raised his head and poured it violently.

With a long sigh of relief, feeling the coldness spread across his chest, he raised his hand and wiped his mouth.

"Thank you."

"You're welcome."

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

Looking at Lu Zhou, who was still a little breathless, she said casually in a casual tone.

"It's not like you."

Lu Zhou grinned: "What are you referring to?" ”

Molina: "Two months ago your physical strength was much better than it is now, and it seems that this holiday has made you slack. ”

When she said this, Mo Lina's tone was a little gloating, although Lu Zhou didn't know what she was gloating.

No matter how lax he was some time ago, with what he has achieved so far, he can still beat 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.

There was no suspense, and his shot hit the bullseye with unbiased bias.

However, his gaze seemed to be glued to the surface of the lake, and he couldn't take it off.

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

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

"You mean there's a bomb under the lake?" Molina raised her eyebrows and said in a teasing tone, "In this country, this joke can't be messed around. ”

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

Molina said as a matter of course: "Of course not...... Anyway, why do you ask? ”

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

Molina burst out laughing.

"It's bizarre."

Staring at the sparkling lake in the sunset, staring at the kayak club members who were training on the lake, Lu Zhou said meaningfully.

"yes, that's bizarre."

But is there a possibility?

For example, if a water molecule in a system moves irregularly at a certain moment, the vector of the motion happens to be outward at the same time? It's like natural volatilization, but because of various coincidences, this "volatilization process" is more intense, and the energy is released in an instant.

However, no matter how you open this brain hole, Lu Zhou can't make up the picture of the kayak on the lake being blown out by the lake water that evaporates instantly.

Unless......

Throw a big bomb or something.

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

Molina asked, "Is the explosion of a still lake on its own also part of the NS equation?" ”

Lu Zhou nodded and said frankly.

"That's right."