Scholar's Advanced Technological System

Chapter 375: In-progress Navier–Stokes Equations Results

Translator: Henyee Translations Editor: Henyee Translations

Ever since Lu Zhou arrived in Princeton, he discovered how normal grinding was.

Deligne had always criticized him for his work and lifestyle. However, Lu Zhou’s desire to solve problems made him this way.

This often reminded him of his high school life.

Whenever he came across a mathematics problem that he couldn’t solve, he would always become obsessed with the problem. He wouldn’t even eat until he had solved the problem.

He had always had this desire to explore the unknown.

Lu Zhou finally completed his thesis at the end of October.

Lu Zhou looked at the stacks of paper on his desk and smiled.

He felt nostalgic at the feeling of solving pure mathematics problems.

Lu Zhou turned on the computer and opened a Word document. He began transferring his work into the computer.

[The Existence of Smooth Solutions of 3D Incompressible Navier-Stokes Equations with Specific Initial Values]

Lu Zhou typed the title and began writing the abstract. He made a summary of his work.

Simply put, he set the initial value of a certain condition α and used a PDE ¹ method to prove the existence of a smooth solution to the three-dimensional incompressible Navier-Stokes equations, under the “α case”.

Prior to this, the study of the existence of the smooth solution of the three-dimensional incompressible Navier-Stokes equations assumed that the initial value of the fluid motion region was small.

As for the existence of the smooth solution to the Navier–Stokes equations when the initial value was large, it was still a mystery.

In some sense, Lu Zhou was adding onto the foundation. He made another step forward to the Millennium Prize Problems.

Interestingly enough, Lu Zhou didn’t intend to go after the Millennium Prize Problems, he only followed Old Qiu’s advice to create a theoretical tool.

Now, not only did he create the theoretical tool, but he also made an in-progress result of the Navier–Stokes equations problem.

This was related to the Millennium Prize Problems. Therefore, the significance of this research wasn’t small.

Lu Zhou was in a dilemma.

Should I post this in a mathematics journal or a physics journal?

This is a problem worth considering.

It’s purely theoretical, I can’t post it on Science or Nature, right?

...

The next day, Lu Zhou brought his laptop to his Institute for Advanced Study office.

He placed his laptop on the table and opened it. He looked at Wei Wen, who was on the other side of the office.

“Wei Wen.”

“What?” Wei Wen adjusted his glasses. He was studying partial differential equations when he heard Lu Zhou.

Lu Zhou waved his hand and said, “Look at this thesis.”

Wei Wen was confused. He stopped writing and walked to Lu Zhou. He looked at the thesis on the laptop screen.

He didn’t react for a long time.

Wei Wen: “...”

When Lu Zhou saw that he didn’t react, he said, “Just roughly look over it, what do you think?”

“I...” Wei Wen lowered his head and said, “Don’t understand.”

Lu Zhou coughed and said, “That’s fine, just give me an opinion. Do you think it’s better to post it on a mathematics journal or a physics journal?”

Wei Wen went silent for a while before he responded hesitantly, “... Mathematics should be good.”

Lu Zhou asked, “Why?”

Wei Wen said, “The calculation part is longer than the discussion part.”

Lu Zhou: “...”

That’s straightforward.

However...

This does seem to make sense?

Mathematics does have more calculations than physics.

Lu Zhou thought for a bit and decided on a mathematics journal.

As for which journal...

Lu Zhou was a Princeton professor, he obviously was going to submit to the Princeton University Journal.

He hadn’t submitted to the Princeton Annual Mathematics journal in a while.

Lu Zhou attached the thesis to his email and sent the thesis to the Annual Mathematics editorial department.

After that, he closed his laptop and went to the Princeton Plasma Physics Laboratory(PPPL).

The theoretical work was nearly complete, Lu Zhou now had to work on the experiment.

...

A modern minimalist-style building surrounded by grass was located in the town of Princeton. It looked ugly compared to the Oxford-style Princeton University buildings.

However, no one could undermine its influence in the nuclear fusion field.

If Lyman Spitzer was able to provide a theoretical blueprint for people to achieve controlled nuclear fusion, then this laboratory was responsible for realizing the blueprint.

Since the beginning of the century, ITER established a framework for various research institutes in the field of controlled nuclear fusion technology. PPPL had been working closely with the Max Planck Institute on research for the stellarator.

The world’s largest prototype stellarator nuclear fusion device, the “Wendelstein 7-X”, was built with the help of PPPL. PPPL also cooperated with several other major nuclear fusion research groups around the globe.

Most people didn’t believe that in addition to controllable nuclear fusion, the researchers here also dealt with neon plasma and even helium plasma accelerators.

Imagine the rocket spacecraft thrusters in Sci-fi movies, that was what they were researching.

Lu Zhou made an appointment in advance and waited in the research institute lounge. Soon after, he saw the head of the laboratory, Sam Lazerson.

When Professor Lazerson heard Lu Zhou’s request, he smiled.

“You plan on designing an experiment to observe high-temperature plasma?”

Lu Zhou nodded. “Yes.”

Professor Lazerson smiled and said, “This is different than mathematics, it’s not that simple.”

“I know,” Lu Zhou shrugged and said, “I only want to consult on some technical issues.”

Lazerson didn’t say anything; he wanted Lu Zhou to continue.

It was obvious that Lazerson treated Lu Zhou as a “non-expert”.

After all, if this thing was that easy, someone would have solved it by now.

However, Lu Zhou wasn’t fazed by the plasma expert’s attitude, and he continued to speak.

“Hypothetically speaking, can we place two ports of plasma on the track and deliver an extraneous particle to the helium and neon plasma through the A port, then recycle the particles through the B port... Is this possible in theory?”

Professor Lazerson touched his chin as he replied, “This does sound interesting, but what is the use of this?”

“It’s difficult to directly observe plasma at high temperatures, but it is mathematically feasible to analyze the trajectories of the plasma colliding with particles.”

Professor Lazerson squinted his eyes, and he didn’t look as condescending as before.

His expression gradually became more and more serious, like he was thinking about the possibility of this idea.

After a long time, Professor Lazerson finally said, “Ordinary particles won’t work!”

“You’re right.” Lu Zhou nodded and smirked as he said, “Its mass must be the same as tritium or similar, so it can be distinguished from the reactants and products.

“Also the most important thing is that it must be stable!”

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