Chapter 411 - Explosive Equation?

Translator:

Henyee Translations

Editor:

Henyee Translations

Lu Zhou and Professor Fefferman reached a consensus on the proof idea, but there was a problem on how to go about constructing this abstract bilinear operator B’.

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

“Nonlinear” partial differential equations were complex.

And the series of problems derived from it was even more complex...

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

Professor Fefferman stared at the calculations on the blackboard and said thoughtfully, “I can guarantee you that we are close to the final result... We are so close.”

Lu Zhou threw the chalk on the podium and nodded at the blackboard.

However, even though he nodded, he wasn’t happy at all. In fact, he looked a bit gloomy.

After a while, Lu Zhou said, “... I feel the same way.”

Professor Fefferman sighed and uncrossed his arms.

“Sometimes failure and success is only an inch apart, you know? I’m even starting to doubt...”

Lu Zhou looked at him.

“Doubt?”

Professor Fefferman nodded and said, “Although we were optimistic that this proposition must be correct, the results tell us that it may not be as perfect as what we think.”

Professor Fefferman spoke in an uncertain tone; it was completely different from when he was lecturing.

This was the first time he had been uncertain at his calculations.

Lu Zhou stared at the blackboard and went silent for a while. After a while, he finally talked again.

“This is ridiculous.”

Professor Fefferman sighed and said, “It is. This is ridiculous... but it’s not illogical.”

He took out a cigarette and lighter from his pocket.

Normally, smoking wasn’t allowed in the conference rooms; smokers had to go to the smoking room.

But this rule didn’t apply when one was doing research.

After all, the Institute for Advanced Study was established for science, and every rule here was made for scholars to do research.

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

The smoke from the cigarette spiraled up into the air.

Soon after, the smoke gradually dispersed and disappeared into the air without a trace.

Professor Fefferman looked at this phenomenon as he spoke confidently.

“The final state of all systems is chaos, just like our equations. The μΔ value explodes as time increases and blasts truth into the universe. When the time variable is magnified, the equation will explode at an unknown point, and the solution will no longer be smooth...”

This point could not be infinite, and it definitely existed.

It was difficult to find its value by using existing mathematical tools. It was just like how the mathematicians could not solve the Navier–Stokes equation. However, it could be proved indirectly... provided that the proof process wasn’t wrong.

Professor Fefferman didn’t say anything else. Instead, he lit up another cigarette and smoked both at once.

Lu Zhou was certain that this wasn’t for science; it was only for Fefferman to relax.

Lu Zhou admitted that this was an uncomfortable feeling.

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

Would a car that was driving on the highway self-disintegrate at a random certain point in time? This was impossible. The worse case was a speeding ticket from the police.

If the conclusion was correct, then the three dimensional Navier–Stokes equation would undoubtedly “explode” past a certain point.

This meant that at some point in time and space, it would no longer retain its regularity...

This was ridiculous!

...

The Navier–Stokes equation research team reached a bottleneck.

At night, Lu Zhou went back to his routine. He put on his running attire and jogged around Lake Carnegie as he tried to relax his mind by breathing in the fresh air.

Unfortunately, he wasn’t able to do so.

The problem that he discussed with Professor Fefferman earlier kept lingering in his mind.

Lu Zhou began to run faster and faster, and without knowing it, he was already sprinting.

He exhausted all of his energy, and his legs felt as if they were becoming heavier. He finally stopped running.

While panting, Lu Zhou walked to the grassy area and sat down.

Suddenly, a can of sports drink was thrown on the grass, and it rolled and stopped next to Lu Zhou.

Lu Zhou looked up and saw Molina in sportswear. She was holding another can of sports drink.

“For you.”

Lu Zhou opened the can and took a big gulp.

He sighed in relief as he felt the cool liquid moving down his chest. He then wiped his mouth.

“Thank you,” Lu Zhou said.

“You’re welcome.”

Molina sat next to Lu Zhou. She opened her can of drink and took a sip.

When she saw that Lu Zhou was still panting, she said, “This isn’t like you.”

Lu Zhou smiled as he asked, “What do you mean?”

Molina said, “You were in much better shape two months ago. I guess you were completely relaxed during the holidays.”

Molina sounded like she was gloating. However, Lu Zhou didn’t know what she was gloating about.

Despite his time off, Lu Zhou could still easily destroy Molina’s supervisor at the IMU conference that was to be held in August this year...

“Maybe.”

Lu Zhou tossed the can into the garbage bin like it was a basketball.

The can swished into the garbage bin.

Lu Zhou began to stare at the lake.

He stayed silent for five minutes. Suddenly, he asked, “Do you think that Lake Carnegie will suddenly explode?”

“Are you saying there’s a bomb under the lake?” Molina raised her eyebrows and said, “You can’t make this joke in this country.”

Lu Zhou shook his head and said, “I meant... under normal conditions.”

Molina said, “Of course not... Why do you ask that?”

Lu Zhou sighed and said, “Because mathematics tells me there’s a possibility of it happening.”

Molina snorted.

“That’s bizarre.”

Lu Zhou looked at the lake water that was sparkling under the sunset as well as the kayaking club members training before he murmured, “Yeah, this is bizarre.”

But, is it possible?

For example, a water molecule in the system that is moving irregularly. Could its vector of motion randomly erupt in chaos? Just like how natural disasters are caused by coincidences where all of the “volatile” energy is released in an instant.

Lu Zhou kept thinking about the lake evaporating in an instant.

It won’t happen unless...

I throw a large bomb in the lake or something.

However, Lu Zhou research obviously didn’t include “external factors”.

Molina asked, “The lake exploding is a part of the Navier–Stokes equation?”

Lu Zhou nodded and replied, “Yes.”