411 The Long-Lost Princeton Town (3/3)

Chapter 411 The Long-lost Princeton Town (33)

In the end, the couplet horizontally criticizing Lu Zhou was not written.

However, as an unexpected harvest, he has made considerable progress in his research on NS equations.

"The Navier-Stokes equation on Euclidean space R3 can be expressed in the form of tμ=△μ+B(μ, μ), where B is a bilinear operator on a divergence-free vector field, and μ obeys the elimination Property =0..."

The tip of the pen was tapped gently on the draft paper, and Lu Zhou, who was muttering to himself, suddenly froze slightly, then shook his head with a smile.

"I agreed not to touch math after I got home, but I still can't control my hands..."

After writing the comments on the draft paper, Lu Zhou stopped the pen in his hand, stood up and stuffed the stack of draft paper into the suitcase, planning to do research after returning to Princeton.

He still has a whole year to do research.

But to spend time with his parents and his family, only he now has this time...

...

For the rest of the time, Lu Zhou didn't worry about work any more, and focused on celebrating the New Year.

After resting for more than half a month, Lu Zhou felt as if he was resurrected with full blood, and his mental outlook glowed a lot.

Especially the meals made by his parents whetted his appetite.

The only regret is that he has a physique that can't grow any flesh. Even if he eats and sleeps every day, his weight still doesn't change.

In this way, we had a relaxed and happy New Year.

After the fifteenth day of the Lantern Festival, Lu Zhou bid farewell to his family, packed his bags, and embarked on the journey to Princeton again.

After taking the high-speed train to the provincial capital, Lu Zhou directly transferred to the subway to the airport.

Sitting in the waiting hall, Lu Zhou, who was brushing his scarf to pass the time, suddenly received a text message from Senior Chen.

Chen Yushan: [Student, when are you going back to school? 】

Seeing the text message, Lu Zhou smiled and poked his finger on the screen to reply.

[I'm about to board the plane soon. 】

Ding--

Received a reply text message soon.

Chen Yushan: [Ah, you didn't wait for me, it's too much]

Lu Zhou: ...?

You didn't tell me in advance that you wanted to go together...

But speaking of it, when did the senior sister learn to be cute.

Seeing the emoji, Lu Zhou thought for a moment that this text message was sent by Xiao Ai.

Fly from the provincial capital to Shanghai by plane, and then fly across the Pacific Ocean from Shanghai.

After more than 20 hours of tossing and turning, Lu Zhou finally dragged his suitcase and walked out of Philadelphia Airport.

In the parking lot outside the airport, his student Jericho drove his Ford Explorer and had been waiting there for a long time.

Seeing Lu Zhou coming from the airport, Jericho waved excitedly and opened the trunk for him.

"Professor, you are finally back, how was your vacation?"

Lu Zhou smiled and said, "It's very pleasant, how about you? How are you doing during my absence?"

Jericho grinned: "It's great, but you're not here, so I always feel that something is missing."

After starting the car, Jericho took Lu Zhou back to the quiet town of Princeton.

There seems to be a kind of magical power flowing in this small town, which can wash away the impetuousness in people's hearts. When Lu Zhou stepped here, he felt that everything was back on track.

Had a rest day at home.

The next day, Lu Zhou got up early, and after breakfast, he went to the Institute for Advanced Study and found Professor Fefferman.

When he arrived at Professor Fefferman's office, besides Fefferman himself, there were several doctoral students he brought with him.

Seeing Lu Zhou appearing at the door, Professor Fefferman stopped the pen in his hand and said kindly, "Did you have a good vacation?"

Lu Zhou: "It's very pleasant. I haven't missed such a long vacation for a long time."

Professor Fefferman: "Really? Then it might be a little busy."

Lu Zhou smiled lightly.

"It's already ready."

As early as a few years ago, the two established the "NS Research Group", and made a lot of progress in the research on the NS equation. Later, because of Lu Zhou's return to China to receive the award, the research temporarily stagnated.

However, during this period of time, although Lu Zhou has been disconnected and fished, Professor Fefferman has not stopped researching, and has been studying the problems encountered by the two people in their previous research.

Standing up from the desk, Professor Fefferman walked to the window and asked abruptly, "Do you smoke?"

Lu Zhou: "No smoking, what's wrong?"

"It's nothing, it's right not to smoke, it's not a good thing," Professor Fefferman took out a cigarette from the cigarette case, lit it with a lighter, and handed it to Lu Zhou, "However, sometimes it will It brings me unexpected inspiration."

After taking the cigarette handed by Professor Fefferman, Lu Zhou pinched it with two fingers, looking at the smoke floating from the cigarette.

The smoke on the cigarette butt is misty upwards, and the shaped column of smoke gradually diverges.

It is like a fluid with a very low viscosity coefficient.

After staring at the nearly burnt cigarette for a while, Lu Zhou vaguely understood something, but he still asked, "What do you want to tell me?"

Professor Fefferman smiled, and said with a pleasant face: "Many times the fluid we study is just like it, from orderly circling to chaotic divergence at the end, from being predictable at the beginning to completely out of control in the end. Even if it is exhausted All mathematical tools cannot describe the evolution of this chaotic state."

Lu Zhou didn't speak, and waited quietly for him to continue.

"I've been thinking about the question you left for a while," walked to the blackboard, Professor Fefferman smiled, picked up the chalk and said while writing, "Last time we got Pμi:= μi-(Δ^-1)·δi·δj·μj, after which I conducted a further analysis and found something more interesting..."

[=-πi∫Λξ1, ξ2, ξ3 (μ(ξ1), v(ξ2), w(ξ3))...]

This is the research result that Lu Zhou showed on the blackboard last time.

However, Professor Fefferman once again made further research on the basis.

"Given a Schwartz divergence-free vector field μ0, time interval I[0, ﹢∞), we proceed to define a generalized solution H10 of the Navier-Stokes equation as, a continuous map obeying the integral equation μ(t) μ → H10df(R3)..."

[μ(t)=e^(t△)·μ0+∫e^(t-t')△B(μ(t'), μ(t'))dt']

【…】

The other two doctoral students in the office glanced at the densely packed calculations on the blackboard, then lowered their heads in a daze, and went on with their own affairs.

The big guys discuss academic issues.

I can't afford it, I can't afford it...

After finally finishing the last line of calculation, Fefferman took back the chalk in his hand and looked at Lu Zhou next to him.

"What do you think?"

After staring at the blackboard for a while, Lu Zhou said.

"Have you constructed a partial differential equation similar to the NS equation?"

"That's right," Professor Fefferman said in a relaxed tone, "construct an abstract bilinear operator B', which has a similar nonlinearity to Euler's linear operator B in μ(t). Linear structure, but at the same time it is different from B."

"If we prove that this stronger conclusion holds..."

Professor Fefferman nodded with a smile: "We can indirectly prove that the original conclusion is also valid!"

Third watch, ask for a monthly ticket~~~~