In the end, Lu Zhou did not manage to write the couplet.
However, as an unexpected reward, his research on the Navier – Stokes equation made some progress.
"The Navier-Stokes equation in Euclidean space R3 can be expressed as? T μ = △ μ + B (μ, μ), where B is a bilinear operator on a divergence free vector field, μ obeys the elimination property B (μ, μ), μ > = 0 … "
Lu Zhou's pen gently tapped on the draft paper as he muttered to himself. Suddenly, he paused for a second and shook his head with a smile.
"I said I wouldn't touch mathematics after I got home, but I can't control my hands …"
Lu Zhou wrote down some comments on the draft paper. He stood up and stuffed the stack of draft paper into his suitcase. He planned to do some research when he returned to Princeton.
He still had a whole year to do research.
As for spending time with his parents and family, only the current him had the time to do so …
…
For the rest of the time, Lu Zhou didn't worry about work anymore and focused on the New Year.
After resting for more than half a month, Lu Zhou felt as if he had been rejuvenated. His entire spirit and appearance were glowing.
Especially the food cooked by his parents, it gave him a great appetite.
His only regret was that he couldn't gain weight no matter how hard he tried. Even if he ate and slept every day, his weight didn't change at all.
Just like that, they had a relaxing and happy New Year.
After the Lantern Festival, Lu Zhou said goodbye to his family, picked up his luggage, and once again embarked on his journey to Princeton.
After taking the high-speed train to the provincial capital, Lu Zhou directly took the subway to the airport.
Lu Zhou was sitting in the departure lounge, scrolling through Weibo to kill time. He suddenly received a text message from Chen Yushan.
Chen Yushan: [Junior, when are you going back to school?]
When Lu Zhou saw the message, he smiled and typed on the screen.
[I'm about to board my plane.]
Ding!
Soon, he received a reply.
Chen Yushan: [Ah, you didn't wait for me? ?]
Lu Zhou: …?
You didn't tell me in advance that you were leaving with me …
Speaking of which, when did Senior Sister learn to act cute?
Seeing the emoji, Lu Zhou thought for a moment that the message was sent by Xiao Ai.
They flew from the provincial capital to Shanghai, and then flew across the Pacific Ocean from Shanghai.
After more than 20 hours, Lu Zhou finally dragged his suitcase out of Philadelphia Airport.
In the parking lot outside the airport, his student Jericho had been waiting in his Ford Explorer for a long time.
When Jerick saw Lu Zhou coming from the airport, he waved excitedly and helped him open the trunk.
"Professor, you're finally back. How was your vacation?"
Lu Zhou smiled and said, "Very happy. How about you guys? How have you been while I was away? "
Jerick grinned. "Very good. It just feels like something is missing when you're not here."
Jerick started the car and took Lu Zhou back to the quiet town of Princeton.
It was as if there was a magical force in this town that could wash away the impetuosity in people's hearts. The moment Lu Zhou stepped into this town, he felt like everything was back on track.
He rested at home for a day.
The next day, Lu Zhou woke up early. After eating breakfast, he went to the Institute for Advanced Study and found Professor Fefferman.
When he arrived at Professor Fefferman's office, other than Fefferman himself, there were also several PhD students in the office.
When Professor Fefferman saw Lu Zhou at the door, he put down the pen in his hand and said, "Did you have a good vacation?"
Lu Zhou: "I did, I haven't had such a long vacation in a long time."
Professor Fefferman: "Really? Then I might be a little busy. "
Lu Zhou smiled.
"I've been preparing for a long time."
The two established the "Navier – Stokes equation research group" and made a lot of progress on the Navier – Stokes equation. However, because Lu Zhou returned to China to receive the award, the research was temporarily stalled.
However, even though Lu Zhou had been slacking off, Professor Fefferman didn't stop his research. He continued to study the problems that the two encountered in their research.
Professor Fefferman stood up from his desk and walked to the window. He suddenly asked, "Do you smoke?"
Lu Zhou: "I don't smoke, why?"
"Nothing, you're right not to smoke, it's not a good thing." Professor Fefferman took out a cigarette and lit it with a lighter. He then handed it to Lu Zhou and said, "But sometimes, it gives me unexpected inspiration."
Lu Zhou took the cigarette from Professor Fefferman and pinched it with two fingers. He looked at the smoke rising from the cigarette.
The smoke at the end of the cigarette floated upwards, and the shaped column of smoke gradually dispersed.
It was like a liquid with a low viscosity coefficient.
Lu Zhou stared at the cigarette for a while and vaguely understood something. However, he still asked, "What are you trying to tell me?"
Professor Fefferman smiled and said, "Most of the time, the fluid we study is just like this. It goes from spiraling in an orderly fashion to disorderly divergence, from being predictable to completely out of control. Even with all of our mathematical tools, we can't describe the evolution of this chaotic state. "
Lu Zhou didn't say anything. Instead, he quietly waited for him to continue.
"Recently, I've been thinking about the problem you left behind." Professor Fefferman walked next to the blackboard and smiled. He picked up a piece of chalk and said, "Last time, we got Pμi: = μi- (Δ ^ -1) · δi · δj · μj. After that, I conducted further analysis and found something more interesting …"
[ = -πιλλξ 1, ξ 2, ξ 3 (μ (ξ 1), v (ξ 2), w (ξ 3)) …]
This was the research result that Lu Zhou showed on the blackboard last time.
However, Professor Fefferman did further research on this foundation.
"Given a Schwarz divergence free vector field μ0, the time interval I? I define a generalized solution of the Navier-Stokes equation, H10, as a continuous mapping μ → H10df (R3) obeying the integral equation μ (t) … "
[μ (t) = e ^ (t △) · μ0 + (e ^ (t-t ') △ B (μ (t'), μ (t ')) dt']
[…]
The other two PhD students in the office looked at the densely packed calculations on the blackboard with muddled expressions. They then lowered their heads and continued with their own work.
The big names were discussing academic problems.
I can't mess with them …
Fefferman finally finished writing the last line of calculations. He put away the chalk in his hand and looked at Lu Zhou.
"What do you think?"
Lu Zhou stared at the blackboard for a while and spoke.
"You constructed a partial differential equation similar to the Navier – Stokes equation?"
"That's right." Professor Fefferman said in a relaxed tone, "I constructed an abstract bilinear operator B '. This kind of bilinear operator has a similar nonlinear structure to the Euler linear operator B in μ (t), but it is different from B.
"If we prove that this stronger conclusion is valid …"
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