Scholar’s Advanced Technological System

Chapter 412: Lu Manifold?

Molina stared blankly at Lu Zhou for around half a minute. Suddenly, she reached out her hand.

Lu Zhou felt that his forehead was about to be touched, and he quickly ducked.

“What are you doing?”

Molina said nonchalantly, “Nothing, I just wanted to see if you’re sick.”

Lu Zhou: “…”

Molina looked at Lu Zhou as she asked in a serious tone, “Seriously, I haven’t studied partial differential equations before, but why are you trying to complicate the problem?”

Lu Zhou patted the grass off his shorts before he stood up.

“I want to make it simple, but I can’t. It’s that complicated.”

Molina stood up, and as she walked in front of Lu Zhou, she said, “If a calculation has violated some basic common sense, then there’s a high probability that it is wrong.”

Lu Zhou didn’t deny her claim.

“Maybe you’re right, I agree with you. However, when it comes to the solution of a three dimensional Navier–Stokes equation, I want to know why…”

Lu Zhou looked at the lake as he continued, “Why our equation exploded…”

…

“Explosion” was also called divergence. At least, they were called so in the field of computational fluid dynamics. Many of these authors also like to use “blew up” as a way to describe this troublesome phenomenon.

Mathematically speaking, an explosion could mean many things, like when the denominator of a solution was 0, or when the matrix solution didn’t converge…

But when it came to the Navier–Stokes equation, exploding meant divergence. It referred to a certain point in time and space where the flow rate of the fluid became faster and faster and moved towards infinity. This violated common sense.

People had proved half a century ago that this point didn’t exist in two-dimensional space, which meant that the Navier–Stokes equation had a unique and stable two-dimensional solution. But no one in the academic community knew what would happen when one applied the Navier–Stokes equation into a three-dimensional system.

The mathematics community was generally optimistic about the existence of a three dimensional smooth Navier–Stokes equation solution. People who were in the field of computational fluid mechanics were also optimistic. Because if a smooth solution didn’t exist, then their phenomenological models would be equivalent to using lies to explain lies.

By the time Lu Zhou returned home, he was drenched in sweat. He threw his clothes into the washing machine and went to take a shower.

The feeling of hot water flowing down his body helped his mind to relax.

The idea of an indirect proof using bilinear operators might be flawed. Therefore, instead of being entangled with an uncertain piece of proof, it might be better to try another proof method.

This type of problem often challenged the limit of the human mind; there was no correct way to solve it.

The differential geometry community never thought about partial differential equations before the Calabi Conjecture was solved. After the Calabi Conjecture was solved, geometric analysis on partial differential equations was born.

Maybe Lu Zhou could discover something even more valuable while he attempted to solve the Navier–Stokes equation?

He went into his study room and opened his computer. He began to search for material on the Navier–Stokes equation.

After all, this was a century-old problem that came with a reward from the Clay Institute. The Navier–Stokes equation had a crucial position in the field of partial differential equations, and therefore, many scholars had produced beautiful research results based on this problem.

Every time Lu Zhou’s research reached its bottleneck, he would try to solve the puzzle by finding research documents.

Just like how Perelman immediately solved the Poincaré conjecture after reading a thesis on the Ricci flow, Lu Zhou was using a similar method.

However…

Finding the piece of the puzzle wasn’t so easy.

The sky outside the window was covered with stars; the clock hit 12 o’clock.

Lu Zhou sighed and leaned against his chair as he pinched his glabella.

His mind was filled with erratic thoughts; he was thinking about writing ink and cigarette smoke. It made his head hurt.

Suddenly, amid this foggy thoughts, Lu Zhou had a slight enlightened moment.

“If I don’t have a tool, why don’t I build one…”

If I take each abstraction of a molecule as a point and collect these points into a Euclidean space, then I can construct an approximate three-dimensional space and use topology…

But this feels like I’m making this “simple” problem even more “complex”.

But I think…

It might work?

Lu Zhou’s eyes lit up.

Lu Zhou grasped firmly on his inspiration and quickly picked up the pen to write down a line of words on the paper.

[Lu Manifold]

After that, he couldn’t stop writing…

…

Time always flew by when Lu Zhou was immersed in research.

In a blink of an eye, it was already April.

Over the past month and a half, Lu Zhou mostly locked himself in his room and had a boring spring break.

During this time, other than when Vera came to his house to give him her lecture report, Lu Zhou had basically cut off all communication with the outside world.

In fact, even though Lu Zhou was the one that asked Vera to give him the lecture report, he hadn’t even read the report once.

Professor Lu had a unique approach to research that even undergrad students had come to know about it from the older students.

Perhaps Professor Fefferman knew that Lu Zhou’s research had gone into a critical stage as he didn’t bother Lu Zhou at all during this period of time. He stopped all regular research exchange meetings and began doing his own independent research.

Lu Zhou finally produced some results.

He stopped writing and looked at the draft paper with a smile on his face.

Lu Zhou’s brain could finally relax, and he began to think of some unimportant things.

Like whether the name “Lu Manifold” was a good name or not?

What if he changed it to “LZ Manifold” or “Lu Zhou Fold”?

Lu Zhou thought about it and decided not to torture future generations.

The former sounded weird and the latter didn’t roll off the tongue well.

“I’ll just stick with Lu Manifold, L Manifold or L Fold for short!”

Lu Zhou was happy with this name. He changed the manuscript title and put the papers aside. He was about to import the contents into the computer.

He then turned on his computer and was about to get to work when a blue notification popped on the corner of his computer screen.

Xiao Ai: [Master, you have mail!]

When Lu Zhou saw this notification, he immediately clicked on the link that Xiao Ai included in its message.

The email was from the Annual Mathematics journal.

It was about the Collatz conjecture.

Lu Zhou read the email from the beginning to the end and smiled.

Although this was expected, he was still sincerely happy for his students.

According to the editorial department at Annual Mathematics, their thesis would be published in the latest issue of the journal. This would allow the mathematics community to read it in its entirety…