In the end, the couplet was not written.

However, as an unexpected gain, his research on the NS equation has made considerable progress.

"The Navier-Stokes equation on Euclidean space R3 can be expressed as ∂tμ=△μ+B(μ,μ), where B is a bilinear operator on a divergence-free vector field, μ obeys the dissolution 〈B(μ,μ), μ〉=0......"

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

"I said that I would no longer touch math when I got home, but I still couldn't control my hands......"

After writing notes on the scratch paper, Lu Zhou stopped the pen in his hand, stood up and stuffed the stack of manuscript paper into his suitcase, intending to wait until he returned to Princeton to do research.

He still has a whole year to do research.

And to accompany his parents and family, only now he has this time......

……

For the rest of the time, Lu Zhou didn't worry about work anymore and concentrated on the New Year.

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

Especially the meals cooked by his parents made him even more appetizing.

The only regret is that he can't grow meat physique, even if he eats, sleeps, sleeps and eats every day, his weight still hasn't changed much.

In this way, I had a relaxed and pleasant New Year.

After the Lantern Festival on the fifteenth, Lu Zhou said goodbye to his family, packed his bags, and embarked on the journey to Princeton again.

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

Lu Zhou, who was sitting in the waiting hall and was brushing his neck to pass the time, suddenly received a text message from Senior Sister Chen.

Chen Yushan: [Senior brother, when will you return to school? 】

Seeing the text message, Lu Zhou smiled and replied with his finger poking at the screen.

[I'm about to board the plane.] 】

Ding——

Received a text message with a reply very quickly.

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 which, when did the senior sister learn to sell cuteness?

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

Flew from the provincial capital to Shanghai, and from Shanghai to the Pacific Ocean.

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

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

Seeing Lu Zhou coming from the airport, Jericho waved his hand excitedly and helped him open the trunk.

"Professor, you're finally back, how was the holiday?"

Lu Zhou smiled and said, "Very pleasant, what about you?" Are you all okay during my absence? ”

Jericho grinned, "It's good, it's just that you're not there, and it always feels like something is missing." ”

Starting the car, Jericho returns to the peaceful town of Princeton with the land boat.

There seems to be a magical magic flowing in this town, which can wash away the impetuosity in people's hearts, and the moment Lu Zhou steps here, it feels like everything is back on track.

Rested at home for a day.

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

When he arrived at Professor Feverman's office, there were several doctoral students he had brought with him, in addition to Feverman himself.

Seeing Lu Zhou appearing at the door, Professor Feverman stopped the pen in his hand and said with a pleasant face: "Did you have a good holiday?" ”

Lu Zhou: "It's very pleasant, I haven't let go of such a long vacation for a long time. ”

Professor Feverman: "Really? Then it might be a bit hectic. ”

Lu Zhou smiled faintly.

"It's been ready for a long time."

As early as a few years ago, the two of them established the "NS Research Group", and a lot of progress was made in the research of NS equations.

However, during this period of time, although Lu Zhou has been dropping the line and fishing, Professor Feverman 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 Feverman walked to the window and suddenly asked abruptly, "Do you smoke?" ”

Lu Zhou: "If you don't smoke, what's wrong?" ”

"It's nothing, it's right not to smoke, it's not a good thing," Professor Feverman said as he took a cigarette out of the cigarette case, lit it with a lighter, and handed it to Lu Zhou, "However, sometimes it also gives me unexpected inspiration." ”

Taking the cigarette from Professor Feverman, Lu Zhou pinched it with two fingers, studying the smoke floating from the cigarette.

The smoke on the cigarette butt ethereated upwards, and the shapely column of smoke gradually dispersed.

It's like a fluid with a very low viscosity coefficient.

Staring at the cigarette that was about to burn out for a while, Lu Zhou vaguely understood something, but still asked, "What do you want to tell me?" ”

Professor Feverman smiled and said kindly: "Many times the fluid we study is like it, from circling in an orderly manner to diverging in a chaotic manner at the end, from the initial predictability to the final complete loss of control. Even if all mathematical tools are exhausted, it is impossible to describe the evolution of this chaotic state. ”

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

"I've been thinking about the question you left behind for a while," Professor Feverman said with a smile as he walked over to the blackboard, picked up the chalk and wrote as he wrote, "Last time we got Pμi:=μi-(Δ^-1)·δi·δj·μj, after which I analyzed it further and found something more interesting......"

【〈B（μ，v），〉=-πi∫Λξ1，ξ2，ξ3（μ（ξ1），v（ξ2），（ξ3））……】

This is the result of the last time Lu Zhou showed the results on the blackboard.

However, Professor Feverman went one step further.

"Given a Schwartz divergence-free vector field μ0 and a time interval I⊂ [0,+∞), I go ahead and define a generalized solution of the Navier-Stokes equation H10 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 looked at the dense calculations on the blackboard with a confused expression, lowered their heads in confusion, and continued to do their own things.

The bigwigs discuss academic issues.

Can't be provoked, can't be provoked......

Finally finishing the last line of the equation, Feverman withdrew 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 spoke.

"You constructed a partial differential equation similar to the NS equation?"

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

"If we prove that this stronger conclusion is true......"

Professor Feverman smiled and nodded: "We can indirectly prove that the original conclusion is also true!" ”