Chapter 410: The long-lost town of Princeton (3/3)

In the end, the couplet horizontal batch of land boats was not written. Fiction.
However, as an unexpected gain, his research on the ns equation has made great progress.
"The navier-stokes equation on Euclidean space can be expressed as t = △ + b (,), where b is a bilinear operator on a divergence-free vector field, obeying the elimination = 0 ……

The tip of the pen was lightly tapped on the draft paper, and Lu Zhou murmured to his mouth, suddenly hesitated slightly, then shook his head with a smile.
"When I got home, I stopped touching math, and I still couldn't control my hands ..."
After writing a comment on the draft paper, Lu Zhou stopped the pen in his hand, stood up, and stuffed the stack of paper into the trunk, intending to return to Princeton to do research.
He still has a whole year to do research.
While spending time with his parents and family, only now he has this time ...
...
During the rest of the time, Lu Zhou did not worry about his work and concentrated on the New Year.
After having rested for more than half a month, Lu Zhou felt like he was resurrected with blood, and the whole person's mental appearance was radiant.
Especially the meals made by his parents made him appetite.
The only regret is that he couldn't grow a flesh constitution, even though he ate and slept every day, his weight remained unchanged.
In this way, a relaxed and happy New Year.
After the fifteenth Lantern Festival, Lu Zhou bid farewell to his family, carried his backpack, and set off on his journey to Princeton again.
I took the high-speed rail to the provincial capital, and Lu Zhou went directly 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 sister Chen Xue.
Chen Yushan: [School brother, when are you going back to school? 】
Seeing the text message, Lu Zhou smiled, and his fingers poked back at the screen.
[I will be boarding soon. 】
I received a reply shortly.
Chen Yushan: [Ah, you didn't wait for me, that's too much]
Lu Zhou: ...?
You didn't tell me in advance to go together ...
But speaking, Xuejie also learned to sell cute.
Seeing that emoji, Lu Zhou thought for a moment that the text message was from Xiao Ai.
He flew from the provincial capital to Shanghai, and then flew across the Pacific from Shanghai.
After more than 20 hours of touring, 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 has been waiting there for a long time.
Seeing the land boat coming from the airport, Jericho waved excitedly and helped him open the trunk.
"Professor, you're finally back. How is your holiday?"
Lu Zhou smiled and said, "Very pleasant, how about you? Are you okay during my absence?"
Jericho grinned, "It's so good, you just don't feel like you're missing anything."
Starting the car, Jericho took the landing boat back to the peaceful town of Princeton.
There seems to be a magical magic flowing in this town, which can wash away the impetuousness in people's hearts. When Lu Zhou stepped in here, I felt that everything was back on track.
Have a rest day at home.
The next day, Lu Zhou got up in the morning, and after breakfast, he set off for the Institute of Advanced Studies and found Professor Fefferman.
When he arrived at Professor Fefferman's office, in addition to Fefferman himself, there were several doctoral students with him.
Seeing the Luzhou appearing at the door, Professor Fefferman stopped the pen in his hand and said cheerfully, "Have a good holiday?"
Lu Zhou: "It's a pleasure. I haven't had such a long vacation in a long time."
Professor Fefferman: "Really? Then maybe a little busy next."
Lu Zhou smiled slightly.
"Already prepared."
As early as two years ago, the "ns research group" was established by the two, and a lot of progress has been made in the research on the ns equation. Later, due to Lu Zhou's return to the country to receive the award, the research has temporarily stalled.
However, since this time, although Lu Zhou has been offline to touch the fish, Professor Fefferman has not stopped researching and has been studying the problems encountered in the previous research of these two people.
Standing up from his desk, Professor Fefferman approached the window and suddenly asked abruptly, "Do you smoke?"
Lu Zhou: "No, what's wrong?"
"Nothing, it's right not to smoke, that's not a good thing," Professor Fefferman took a cigarette out of the cigarette case, lit it with a lighter, and passed it to Lu Zhou. "But sometimes it also Give me unexpected inspiration. "
After receiving the cigarette from Professor Fefferman, Lu Zhou pinched with and looked at the smoke rising from the cigarette.
The smoke on the cigarette swelled upward, and the shaped plume gradually diffused.
It's like a fluid with a very low viscosity coefficient.
Staring at the nearly exhausted cigarette for a while, Lu Zhou vaguely understood something, but still asked, "What do you want to tell me?"
Professor Fefferman smiled and said with Yue Yueyan: "Many times the fluid we are studying is like it, from orderly circle to the final disorderly divergence, from the initial predictable to the end completely out of control. Even if exhausted No mathematical tool can describe the evolution of this chaotic state. "
Lu Zhou did not speak, waiting quietly for him to continue.
"Since this time, I have been thinking about the problem you left," Professor Fefferman walked to the blackboard, smiled, picked up the chalk and wrote, "Last time we got pi: = i- (Δ ^ -1) δiδjj, after which I went further and found something more interesting ... "
[ =-πi∫Λξ1, ξ2, ξ3 ((ξ1), v (ξ2), w (ξ3)) ...]
This is the research result that Lu Zhou showed on the blackboard last time.
However, Professor Fefferman has done further research based on this.
"Given a Schwartz non-divergence vector field 0 and time interval i [0, ∞), we continue to define a generalized solution h10 of the navier-stokes equation as a continuous mapping obeying the integral equation (t) → h10df () ... "
[(T) = e ^ (t △) 0 + ∫e ^ (t-t \ ') △ b ((t ’), (t \')) dt \ ']
[……]
The other two doctoral students in the office glanced grimly at the dense calculations on the blackboard ~ EbookFREE.me ~ and lowered their heads with a grimace and went on to their own business.
Big guys discuss academic issues.
Can't afford to mess with ...
After finally writing the last line of calculations, Fefferman retracted the chalk in his hand and looked at the nearby Lu Zhou.
"What do you think?"
Staring at the blackboard for a while, Lu Zhou said.
"You constructed a partial differential equation similar to the ns equation?"
"Yes," Professor Fefferman said in a light tone. "Construct an abstract bilinear operator b \ ', which is similar to the Euler linear operator b in (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 prove indirectly that the original conclusion is also true!"