Chapter 409

Lu Zhou and Professor Fefferman reached a consensus on the proof idea. However, how to construct this abstract bilinear operator B 'became a very serious problem.

It had to have a similar nonlinear structure to the Euler linear operator B in μ (t), but at the same time, it was different from B.

In partial differential equations, "nonlinear" meant complex.

The series of problems that arose from it were the most complex of all problems …

The first meeting in March. A small conference room at the Princeton Institute for Advanced Study.

Professor Fefferman looked at the calculations on the blackboard and spoke.

"I am sure that we are very close to the final result, just a little bit more."

Lu Zhou threw the chalk on the podium and took two steps back. He stared at the blackboard and nodded.

However, even though he nodded, he didn't look happy at all. Instead, he looked at the calculations in front of him with a dignified expression.

After a while, Lu Zhou spoke.

"… I feel the same way."

Professor Fefferman sighed and unfolded his arms.

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

Lu Zhou looked at him with a questioning look.

"Suspect?"

Professor Fefferman nodded and said, "Even though we were optimistic at the beginning that the proposition must be correct, more and more results are telling us that it may not be as perfect as we think."

Professor Fefferman's tone was full of uncertainty. He didn't have the calmness that he usually had in front of his students in class.

After so many years, this was the first time that he had such an uncertain expression on his face.

Lu Zhou stared at the blackboard and went silent for a while before he finally spoke.

He then spoke with difficulty, "This is ridiculous."

Professor Fefferman sighed and said, "Yeah, it's ridiculous, but … it's not unreasonable."

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

In principle, smoking was not allowed in the conference room. Smokers had to go to the designated smoking room.

However, if it was for research purposes, this rule could be ignored.

After all, the Institute for Advanced Study was established for science. All of the rules here were to serve science, to make it more convenient for scholars to research science.

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

The smoke spiraled upward.

After a brief moment of entanglement, the gradually expanding smoke column finally dissipated in the air, leaving no trace behind.

Professor Fefferman stared at this phenomenon and spoke to himself as if he was trying to convince himself.

"All systems that can be predicted will end up in chaos, just like our equations. The value of μΔ, which explodes with time, coincides with the truth of the universe in a sense. When the time variable is magnified, our equation will explode at an unknown singularity, and it will no longer be smooth … "

This special point wasn't infinite, but it seemed to exist.

It was difficult to solve its value with existing mathematical methods, just like how mathematicians couldn't solve the Navier – Stokes equation. However, through indirect proof, it could be proved that it did exist … If the proof process was correct.

Professor Fefferman didn't say anything else. Instead, he silently smoked one cigarette after another.

Lu Zhou was certain that this wasn't for science, it was for venting his frustrations.

He had to admit that this was a difficult thing to accept.

The results of the calculations were clear, but it deviated from common sense.

Would a car driving on the highway self-destruct at a certain point in time without warning? This was obviously impossible. Even in the worst case scenario, it would only be a ticket from the traffic police.

If their conclusion was correct, then the three-dimensional Navier – Stokes equation would undoubtedly "explode" at a certain point.

And this also meant that at this point in time or space, it might no longer have the regularity …

This was ridiculous!

…

The Navier – Stokes equation research had reached an unexpected bottleneck.

At night, Lu Zhou returned to his normal lifestyle. He changed into his sportswear and jogged along Lake Carnegie. He tried to breathe in the fresh air and relax.

Unfortunately, he didn't get what he wanted.

The problem that he discussed with Professor Fefferman in the afternoon was still lingering in his mind.

Lu Zhou's running speed became faster and faster, and before he knew it, he began to sprint.

It wasn't until he exhausted all of his energy that his legs felt as heavy as lead that he gradually stopped.

Lu Zhou panted heavily as he walked to the lawn by the lake and sat on the ground.

Suddenly, a sports drink was thrown from the side. It smashed onto the soft lawn and rolled to his hand.

Lu Zhou looked up and saw Molina, who was wearing sportswear, standing not far away. She was holding another drink in her hand as she waved at him.

"For you."

Since she said this, Lu Zhou didn't refuse. He opened the can and took a big gulp.

He let out a long sigh of relief. Feeling the coldness spreading through his chest, he raised his hand and wiped his mouth.

"Thank you."

"You're welcome."

Molina sat down next to him and took a sip of her drink.

She looked at Lu Zhou, who was still breathing heavily, and spoke in a casual tone.

"This isn't like you."

Lu Zhou smirked and said, "What do you mean?"

Molina: "You were a lot stronger two months ago. It looks like you slacked off during the holidays."

Molina spoke in a gloating tone. However, Lu Zhou didn't know what she was gloating about.

Even if he had slacked off a while ago, with his current achievements, he could still defeat her and her supervisor at least twice at the ICM conference this August …

"Maybe."

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

Without any suspense, his shot hit the bullseye without any deviation.

However, it was like his eyes were glued to the lake; he couldn't look away.

After five minutes of silence, Lu Zhou suddenly spoke.

"Do you think Lake Carnegie will suddenly explode?"

"You're saying there's a bomb buried under the lake?" Molina raised her eyebrows and said in a mocking tone, "In this country, you can't joke about this."

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

Molina said matter-of-factly, "Of course not … Why do you ask?"

Lu Zhou sighed and said, "Because my mathematics is telling me that this is a possibility."

Molina burst out laughing.

"This is too weird."

Lu Zhou stared at the sparkling lake under the setting sun. He stared at the kayaking club members training on the lake as he spoke meaningfully.

"Yeah, this is too weird."

But is this possible?

For example, the water molecules moving irregularly in the system, and the vectors of the movement happened to move outward at the same time? It was like natural volatilization, but due to various coincidences, this "volatilization" process was more intense, and the energy was released in an instant.

However, no matter how hard Lu Zhou tried, he couldn't imagine the scene of the kayaks being blown away by the evaporating water.

Unless …

He threw a large bomb into the water or something.

However, what he wanted to discuss was obviously not this special case of "adding experience parameters".

Molina asked, "Is the explosion of the still lake also part of the Navier – Stokes equation?"

Lu Zhou nodded and spoke frankly.