Scholar’s Advanced Technological System

Lu Zhou didn’t end up writing the third line for the couplet.

However, he made some unexpected progress on his research on the Navier–Stokes equation.

“The Navier-Stokes equation on the Euclidean space R3 can be expressed as ∂tμ = Δμ + B (μ, μ), where B is a bilinear operator on the vector field without divergence, and μ obeys elimination <B(μ,μ),μ>=0…”

Lu Zhou quickly wrote it down on the draft paper while muttering to himself. Suddenly, he stopped and shook his head.

“I said I wouldn’t touch mathematics when I’m home, but I can’t control myself…”

Lu Zhou stopped writing. He shoved the draft paper into his suitcase, and he planned to continue with the research when he was back at Princeton.

He had an entire year to do all the research he wanted.

But he could only be with his family right now…

…

Lu Zhou didn’t do any research at all for the rest of the holiday. Instead, he focused on having a great vacation.

Lu Zhou took a half a month break and felt full of energy; his entire soul felt resurrected.

The home-cooked meals had enhanced his appetite.

Unfortunately, he couldn’t gain any weight no matter how much he ate.

The Lus had a relaxing and happy Chinese New Year.

After Chinese New Year was over, Lu Zhou bade farewell to his family and went back to Princeton.

Lu Zhou got on the high-speed train. He then got onto the subway and headed to the airport.

While Lu Zhou was sitting in the terminal and scrolling through Weibo to kill time, he suddenly received a text from Chen Yushan.

Chen Yushan: [Little Brother, when are you going back to school?]

When Lu Zhou saw the message on his screen, he typed a reply.

[I’m about to board the plane.]

Ding!

Lu Zhou quickly received a reply.

Chen Yushan: [Ah, you didn’t wait for me, how could you! 🙁 ]

Lu Zhou: …?

You didn’t tell me that you wanted to fly together…

But speaking of which, when did Chen Yushan start acting cute?

Lu Zhou looked at the text message and almost thought it was from Xiao Ai.

He got on the plane to fly to Shanghai. From Shanghai, he flew over the Pacific Ocean.

After more than 20 hours of flying, Lu Zhou finally dragged his suitcase out of Philadelphia airport.

His student Jerick was in his Ford Explorer, and he was waiting outside at the airport parking lot. In fact, Jerick had been waiting for a while.

When he saw Lu Zhou walking out of the airport, he waved his hand excitedly before popping open the car trunk.

“Professor, you’re finally back! How was your holiday?”

Lu Zhou smiled and said, “It was great, how about you guys? Are you guys doing okay during my absence?”

Jerick smiled. “Very good, but it feels like something is missing when you are gone.”

Jerick started the car and drove Lu Zhou back to the quiet town of Princeton.

This town had a magical vibe, and Lu Zhou could feel himself getting back into the zone.

Lu Zhou rested at home for the day.

The next day, he woke up early and had breakfast before he went to the Institute for Advanced Study to look for Professor Fefferman.

When he arrived at Professor Fefferman’s office, he saw some of Fefferman’s PhD students there.

The moment Professor Fefferman saw Lu Zhou in front of his office door, he immediately stopped writing as he said in a cheerful tone, “How was your holiday?”

Lu Zhou replied, “Pretty good, I haven’t had a long holiday in a while.”

Professor Fefferman said, “Yeah? It might start to get busy from here on.”

Lu Zhou smiled slightly.

“I’m prepared for it.”

The two set up a Navier–Stokes equation research team a while ago and made quite a lot of progress on the Navier–Stokes equation. However, Lu Zhou had to return to China for the award, and the research was temporarily paused.

However, even though Lu Zhou was on holiday, Professor Fefferman didn’t stop researching. In fact, he had been studying the problems they encountered during the research.

Professor Fefferman stood up from his desk and went to stand next to the window. He asked abruptly, “Do you smoke?”

Lu Zhou replied, “I don’t, why?”

“Nothing, it’s good not to smoke,” Professor Fefferman said as he lit up a cigarette. He handed Lu Zhou the cigarette before he said, “But sometimes, it gives me inspiration when I least expect it.”

Lu Zhou took the cigarette from Professor Fefferman and looked at the smoke coming out of the cigarette.

The smoke from the cigarette slowly floated upward and gradually dispersed.

It was like a liquid with a low viscosity coefficient.

Lu Zhou stared at the burning cigarette for a while before he asked, “What do you want to tell me?”

Professor Fefferman smiled and said, “Often, the liquid we study is just like this. Its Brownian motion diverges, and it completely loses its predictability. Even mathematics can’t explain this chaotic state.”

Lu Zhou didn’t say anything. Instead, he patiently waited for Fefferman to finish.

“Recently, I’ve been thinking about the question you left behind,” Professor Fefferman said as he walked to the blackboard. He then smiled as he picked up a piece of chalk and said, “Last time, we got Pμi:= Ii-(Δ^-1)·δi·δj·μj. I did some analysis on it and found something interesting…”

He then wrote on the blackboard.

[ <B(μ,v),w〉= -πi∫Λξ1,ξ2,ξ3(μ(ξ1),v(ξ2),w(ξ3))…]

This was Lu Zhou’s research result which he wrote on the blackboard last time.

But Professor Fefferman did some further research.

“Given a Schwarz non-dispersive vector field μ0, time interval I ⊂ [0, + ∞), we define a generalized solution H10 of the Navier-Stokes equation as continuous obedience integral equation μ(t) Map μ→H10df(R3)…”

He wrote again on the blackboard.

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

[…]

As the two PhD students in the office looked at the blackboard, they were confused by what they were seeing. They then looked away and focused on their own work.

Geniuses working on a problem…

I can’t understand it…

Fefferman finished writing the last line of calculations and put the chalk down. He then looked back at Lu Zhou.

“What do you think?”

Lu Zhou stared at the blackboard for a while before he asked, “You constructed a partial differential equation that’s similar to the Navier–Stokes equation?”

“That’s right!” Professor Fefferman said in a relaxed tone, “I constructed an abstract bilinear operator B’, which has similarities to the Euler linear operator B in μ(t), but it is also different than B.”

“If we prove this stronger conclusion is true…”

Professor Fefferman smiled and said, “Then we can prove the original conclusion is also true!”