376 Stage Results Of The NS Equation (3/3)

Chapter 376 Phased Results of NS Equation (33)

After coming to Princeton, Lu Zhou suddenly found that exploding his liver seemed to be a common thing for him.

Although Deligne always criticized his lifestyle as a joke about his health, in fact, even if Lu Zhou didn't do it deliberately, his desire to solve the problem would prompt him to do it.

This feeling often reminds him of his high school life.

When encountering a math problem that cannot be solved, I always feel that it is a lump in my heart. If I cannot solve it, I will not even have the motivation to go to the cafeteria to eat.

In essence, this desire to explore the unknown seems to be the same?

As the tail of October is about to slip away, this thesis is finally complete.

Looking at the stack of papers on the table, Lu Zhou smiled comfortably.

He still misses the feeling of returning to the study of purely mathematical problems after a long absence.

Turning on the computer, Lu Zhou began to edit the document and input his work during this period of time into the computer.

"Research on the global existence of smooth solutions of three-dimensional incompressible Navier-Stokes equations under specific initial values"

After typing a line of titles, Lu Zhou began to edit the summary of the full text, and made a summary description of the work during this period.

To put it simply, by setting an initial value that satisfies a specific condition α, he used the PDE method to prove the overall existence of the smooth solution of the three-dimensional incompressible Navier-Stokes equation under the "α case", and some specific conditions satisfy smoothness.

Prior to this, the research on the overall existence of smooth solutions of the three-dimensional incompressible Navier-Stokes equations has only advanced to "under the assumption that a certain norm of a given initial value is appropriately small or the fluid motion area is appropriately small, the NS Existence of a global smooth solution to the equation" step.

As for the overall existence of smooth solutions of the NS equation when the initial value is infinitely smooth and has compact support, it is still a mystery.

In plain language, what Lu Zhou has done is, on this basis, a step forward towards solving the "seven millennium problems" of Mount Everest.

It's quite interesting to say that Lu Zhou didn't rush to solve this millennium problem at the beginning, but set a phased goal according to Mr. Qiu's suggestion, and worked hard to solve the problem while moving towards this goal. theoretical tool.

Now that the theoretical tools have been created, the result is not only the creation of theoretical tools, but also the problem of NS equations, and achieved a phased result.

And because it is related to the big proposition of the millennium problem, the weight of this research result is not small.

But at this time, Lu Zhou was in a difficult situation.

Should this stuff be published in physics journals or in mathematics journals?

This is a question worth thinking about.

Purely theoretical research can't still be published in "Science" and "Nature", right?

...

The next day, with his laptop on his back, Lu Zhou went to the office of the Institute for Advanced Study.

Putting the laptop on the table and turning it on, Lu Zhou looked at Wei Wen who was sitting on the side of the office.

"Wei Wen."

"What's the matter?" Pushing his glasses, Wei Wen, who was brushing up the knowledge of partial differential equations in the literature, raised his head and cast a questioning look at Lu Zhou.

Lu Zhou beckoned: "You take a look at this paper."

Filled with questions, Wei Wen stopped the pen in his hand, got up and walked to Lu Zhou, and looked at the paper on the screen.

As a result, there was no response for a long time.

Wei Wen: "..."

Seeing that he didn't respond for a long time, Lu Zhou urged: "It's enough to take a rough look, give me an evaluation?"

"I..." Wei Wen opened his mouth and lowered his head heavily, "I don't understand."

Lu Zhou was slightly stunned, and coughed lightly: "It's okay, you can simply give an opinion, do you think it is more appropriate to post it in a mathematics journal, or it is more appropriate to post it in a physics journal."

Wei Wen was silent for a while, and reluctantly gave an answer.

"... Then let's do math."

Lu Zhou: "Why?"

Wei Wen immediately said: "The space for calculation is more than the space for discussion."

Lu Zhou: "..."

The reason is quite straightforward.

but……

Seems to make sense?

In terms of the difficulty of reviewing, mathematics journals are relative to physics journals.

Lu Zhou thought about it, and finally decided that it would be more appropriate to post it in a mathematics journal.

As for which journal to choose...

In line with the principle of not letting the fat and water flow to outsiders, Lu Zhou, a professor at Pudong University, naturally published it in the Pudong University magazine.

Speaking of which, since he became a professor here, he has not contributed to the "Annual Journal of Mathematics" for a long time.

After posting the paper in the email, Lu Zhou sent the manuscript to the mailbox of the editorial department of "Annual Mathematics" through the internal submission channel.

Once the submission was done, he closed his laptop and headed to the Princeton Plasma Physics Laboratory (PPPL).

Theoretical preparations have almost been completed, and what Lu Zhou needs to solve now is the experimental problem.

...

Located in the corner of the small town of Princeton, this modern minimalist-style building surrounded by lawns looks unremarkable compared to the adjacent campus that inherits the legacy of Oxford.

But in the field of controlled nuclear fusion, no one can ignore its influence.

If Lyman Spitzer provided people with a theoretical blueprint that can realize controllable nuclear fusion, then it is the research team of this laboratory that turned this theoretical blueprint into engineering drawings.

Since the beginning of the century, the ITER International Cooperation Organization was established, establishing a research framework for controllable nuclear fusion technology for scientific research institutions in various countries. PPPL has cooperated closely with the German Max Planck Society on stellarator research.

The world's largest stellarator controllable nuclear fusion device "Helix 7-X" is the technical service provided by PPPL. At the same time, PPPL also maintains close cooperation with several major controllable nuclear fusion research units in the world. .

Many people may not believe it. In addition to the basis of controllable nuclear fusion, scholars here seem to be not satisfied with the constraints of deuterium and tritium plasma, and even research on xenon plasma accelerators.

If it is difficult to understand, you can imagine the plumes ejected by the Hall effect thrusters on the spacecraft in those science fiction movies, and you can probably understand what black technology it is.

Because he had made an appointment in advance, Lu Zhou quickly met the person in charge, Professor Sam Lazelson, in the lounge of the institute.

After listening to Lu Zhou's intentions, Professor Lazersson smiled.

"Are you planning to design an experimental instrument for observing high-temperature and high-pressure plasma?"

"Yes." Lu Zhou nodded without denying it.

Professor Lazersson smiled, looked at him and said, "This is different from a math problem, it can't be created just by talking about it."

"I know," Lu Zhou shrugged, "I just want to consult some technical matters."

Lazelson didn't speak, but just signaled Lu Zhou to continue with his eyes.

It can be seen that he didn't take the "layman" Lu Zhou's nonsense seriously.

After all, if this thing is really so easy to solve, it won't be delayed until now.

However, Lu Zhou didn't care about the contemptuous attitude of the plasma expert and continued.

"Can I make a hypothesis, set up two ports on the plasma orbit, send an irrelevant particle into the deuterium and tritium plasma through the A port, and then recover the particle through the B port... I want to know, in theory Is such a design achievable?"

Professor Lazelson touched his chin and asked, "This sounds...interesting, but what's the use of doing it?"

"It is very difficult to directly observe the high-temperature and high-pressure plasma, but I think it is mathematically feasible to analyze its trajectory in the plasma by analyzing the particle collision data and waveform changes."

Frowning slightly, Professor Razelson restrained his contemptuous expression on his face.

Gradually, his expression became serious, as if he was thinking about the possibility of this train of thought.

After a long time, Professor Lazersson spoke.

"Ordinary particles probably won't work!"

"You're right," Lu Zhou nodded, with a smile on the corner of his mouth, "Its mass must be similar to tritium or deuterium, and it must be different from the reactants and products in the DT reaction system. Recycle……"

"And most importantly, it must be stable enough!"