A genius? I just love studying.

Chapter 192 Visiting Elder Qiu, Navier-Stokes Equations
"How did you come?"

Qiu Chengwu stood up with a big smile to greet him.

Ok?
Does Mr. Qiu know him?

The tall, thin boy who had hidden to the side stared wide-eyed.

"Could he be Chen Shen—Chen Hui?!"

Given his young age and Old Qiu's attitude, it's not hard to guess the identity of this young man.

Of course he had seen Chen Hui's photo, but people on screen are always distorted. If he didn't frequently hold the photo up to his eyes, it would be difficult to tell the difference if he met him in real life.

Especially this young man in front of me, he looks much, much younger than he does on screen!

Thinking about his earlier advice, Hu Hongfei's face turned slightly red.

Chen Hui, oblivious to the boy's inner thoughts behind him, smiled and said, "I've encountered some math problems and would like to ask Professor Qiu for advice. I wonder if Professor Qiu has the time?"

"Tell me, what's the problem?"

Qiu Chengwu laughed heartily, "There's plenty of time!"

Chen Hui came to him instead of asking Tian Yang about his academic problems, which naturally made him very happy.

"This is?"

At this moment, Qiu Chengwu noticed the tall, thin boy hiding behind Chen Hui. He felt that the boy looked familiar, but he couldn't remember his name for a long time.

"Hu Hongfei, a graduate student at the Mathematics Center, is conducting research on the application of partial differential equations in condensed matter physics under the guidance of Professor Yun Wei."

The tall, thin boy stood up straight and excitedly introduced himself.

"I couldn't find my way earlier, so this classmate led me here," Chen Hui explained.

"Come in and sit down!"

Qiu Chengwu beckoned and went to the cabinet opposite his desk to take out a can of tea.

Hu Hongfei waved his hand repeatedly, "I don't need it, I'll be going now."

"Since you're already here, please have a seat."

Qiu Chengwu said with a smile, like a kind neighbor grandfather.

It's hard to refuse.

Hu Hongfei had never met Qiu Chengwu who was so easy to talk to.

Chen Hui had already gone to the side and boiled a pot of water in an electric kettle.

Qiu Chengwu watched this scene with a smile, then stepped onto the office sofa and sat down before speaking, "Have you been researching the Yang Mills mass gap problem lately?"

The Yang-Mills equation is also a partial differential equation, and he considers himself to have some expertise in partial differential equations, so Chen Hui must have come to him because of the Yang-Mills equation.

But Chen Hui shook his head. "What does Professor Qiu think of the Navier-Stokes equations?"

Qiu Chengwu was taken aback for a moment, then laughed.

He knew that Chen Hui had gone to the Luzhou Plasma Institute, but he really didn't expect that Chen Hui would actually be interested in the Navier-Stokes equations. He was truly a fearless young man!
“Recently, Dennis Sullivan has approached the topic from a topological perspective, proposing to use vorticity instead of velocity field as an intrinsic property of fluids, and to view fluids as elastic media. He believes that vorticity endows structures and may bypass the singularity problem in traditional velocity field analysis. Do you think this shift in perspective has the potential for a breakthrough?”

Chen Hui began to explain that he had conducted in-depth research last night, studying several papers. On the flight to Beijing, he also studied several papers again, and now he had a general understanding of the Navier-Stokes equations.

He is now increasingly aware of the importance of judgment. He can help Chen Hui judge whether a certain direction is feasible. For other mathematicians, this is called mathematical intuition!
He used to think that insight was mathematical intuition, but insight is the ability to walk faster and better on the right path and to more easily see the essence behind phenomena. Judgment is the ability that leads him to the right path!
It's difficult to add more points in a short period of time, but sometimes, he doesn't need to rely on his own strength to solve problems.

Chiu Cheng-wu smiled without saying a word, and advised, "Mathematicians have limited energy. Why not focus your time and energy on the Yang-Mills equations, which you're already starting to understand?"

"The prospect of controlled nuclear fusion is fascinating, but this is not something that any one scientist can change. The breakthrough in the Yang-Mills equation has also made a huge contribution to the academic community, and its prospects are equally fascinating."

"The mass gap problem is still my main focus at present, but it's not a bad thing to think about the Navier-Stokes equations occasionally in my spare time as a dessert after dinner."

Chen Hui clearly had his own ideas.

"Topology tools do offer new paths, but the challenges are enormous."

Qiu Chengwu stopped trying to persuade him, saying, "Feng's team has already used Galerkin approximation to prove the existence of p-Navier-Stokes weak solutions. Perhaps we can try to generalize from local to global solutions."

What about numerical computation?

Chen Hui continued, “Like Neustupa constructing weak solutions in time-varying domains, or Longobardi handling complex flows through linearization.”

Chiu Cheng-wu shook his head. “Numerical results inspire theory, but they are fundamentally different. For example, the nano-slip boundary condition for superhydrophobic surfaces is effective in experiments, but the mathematical convergence of the inviscid limit was not rigorously proven by Ancona’s team in Sobolev space until 2012.”

Chen Hui fell into deep thought.

Just then, the water boiled.

Qiu Chengwu did not disturb Chen Hui. He got up, picked up the teapot, and poured boiling water into it. The dried tea leaves slowly unfurled, like tender buds stretching out in spring.

Hu Hongfei suddenly regretted his decision to stay.

Listening to the two big names discussing academic issues, the first thing they talked about was the Millennium Problem, which left him, a Muggle, completely unable to join in or even understand.

And what about desserts after dinner? Even Hilbert would have to give that a thumbs up!

He felt like an idiot, truly feeling like he was sitting on pins and needles, like he had a thorn in his back, like he had a fishbone stuck in his throat. He just wanted to end this torment as soon as possible.

Chen Hui also got up, picked up the marker under the whiteboard in the office, and wrote down the momentum conservation equation of the Navier-Stokes equations: ρ(tu+uu)=p+μ2u+f.

Qiu Chengwu also stared at the equations on the whiteboard.

For a moment, the office fell silent as the two men fell into deep thought. Only Hu Hongfei longed to escape, but he couldn't.

"This convective term is like a wild horse."

Suddenly, Qiu Chengwu spoke up, "Back when I was solving the Calabi conjecture, it took me a full seven years to find a way to tame Ritchie curvature."

He got up and went to the whiteboard, his thin fingers tracing the interwoven Γ symbols on the whiteboard, as if caressing the ancient stone carvings on the Silk Road eroded by wind and sand.

Chen Hui also shared his thoughts: "Perhaps we shouldn't be fixated on directly proving the smoothness of the solution, but rather, like you did with the Keller-Einstein metric, construct weak solutions on specific fiber bundles?"

"Go on."

A thoughtful look flashed across Qiu Chengwu's eyes. He picked up another marker and quickly wrote next to the sticky item.

Qiu Chengwu's formula gave Chen Hui some inspiration. He felt his brain became much more active and his eyes shone brightly. "The singularity of turbulence may correspond to a sudden change in the topology of the manifold."

"Just as you use geometric surgery to deal with manifold degeneration, can we use algebraic topology tools to establish classification criteria for vortices?"

Chen Hui spontaneously wrote a series of formulas on the whiteboard.

After some thought, Qiu Chengwu made some modifications to Chen Hui's formula.

The two of them started discussing back and forth, and more and more formulas appeared on the whiteboard, soon covering the entire whiteboard.

The tea leaves on the coffee table had fully unfurled, and the tea soup had gradually changed from white and transparent to yellow.

Hu Hongfei's eyes, standing beside him, also grew increasingly confused.

He didn't know how much time had passed. Qiu Chengwu stopped writing with his marker, thought for a long time, and finally shook his head. "Back then, Perelman told me that energy dissipation is like autumn leaves falling—now it's your turn, young people, to catch these falling leaves!"

Chen Hui nodded.

Old Qiu didn't give him an answer, but the discussion still gave him something. At least, it solidified some of his ideas. The next step was to verify them.

Back on the sofa, Qiu Chengwu, his mouth dry, picked up his teacup and took a big gulp of tea. The tea, which had already gone cold, was just right and helped to relieve his irritability.

It was just a waste of his unbranded tea.

"If the regularity and smoothness of the solutions to the Navier-Stokes equations are proven, can turbulence be completely described?"

Seeing that the bigwigs had finished their discussion, Hu Hongfei was finally able to chime in.

Qiu Chengwu looked at Hu Hongfei, then at Chen Hui, and couldn't help but sigh. "Even if we prove the existence of a smooth solution, the complex dynamics of turbulence may still make practical calculations infeasible. The computational resource requirements for full three-dimensional numerical simulation far exceed current capabilities. More fundamentally, can the equations truly cover all fluid behaviors?"

"Of course, from Stokes' classic derivation to Sullivan's topological innovation, every step has expanded the boundaries of human cognition—perhaps the answer itself is not as valuable as the revolution in mathematical tools brought about by the exploration process!"

Qiu Chengwu looked at Hu Hongfei, "So even if we can't describe turbulence, the study of the Navier-Stokes equations is still of great significance!"

"?"

A big question mark appeared above Hu Hongfei's head. "I was just asking casually, why are you looking at me like that?"
You don't actually think I can solve the Navier-Stokes equations, do you?
Afterwards, Chen Hui chatted with Qiu Chengwu about some non-academic issues and sampled the food at Tsinghua University's canteen before leaving Tsinghua Garden and heading towards Yanbei University across the street.

"Chen Shen, have you solved the mass gap problem in Yang-Mills equations? Are you going to start researching the next Millennium Problem?"

After parting ways with Qiu Chengwu, Hu Hongfei became lively again, excitedly asking Chen Hui all sorts of questions.

"No."

Chen Hui shook his head, "No need to call me God Chen, just call me Chen Hui."

Although he had seen netizens addressing him this way online, he still felt somewhat uncomfortable when he encountered it in real life.

"I believe you can do it," Hu Hongfei said with a determined look, appearing even more confident than Chen Hui himself.

"Thank you." Chen Hui smiled; he felt the same way.

"Chen Shen, can we take a picture together?"

Hu Hongfei asked somewhat nervously, "Let me absorb some of your talent, and hurry up and publish a Q1 SCI paper!"

"of course can!"

Chen Hui voluntarily stepped into Hu Hongfei's mobile phone camera frame.

……

"That great mathematician has left?"

At the Luzhou Plasma Institute, Xu Guofu rushed into Song Yuntao's office, asking with a regretful expression.

"Left early in the morning."

"Pity!"

Xu Guofu sighed with regret, "If only I had asked him to leave his autograph, it might have become a family heirloom in the Xu family."

Song Yuntao rolled his eyes. "Luckily he left early!"

"That's not fair. The reason I missed this opportunity was to prepare for the experiment."

Xu Guofu said, grumbling, "But is there any hope for that matter?"

Song Yuntao also withdrew the sarcastic remark that was on the tip of his tongue. His old friend had indeed worked hard these past two days.

"Who knows."

"Even if there is a breakthrough, it won't be something that can be accomplished in a short time, so we shouldn't count on him. Let's continue the experiment according to the original plan. It would be best if he could make a breakthrough, but even if he can't, we still need to overcome those difficulties one by one!"

Song Yuntao's eyes were firm.

"of course!"

Xu Guofu also chimed in, "However, I'm still somewhat looking forward to room temperature superconductivity."

"I really look forward to that day!"

Song Yuntao finally couldn't help but roll his eyes again. "If you're tired, go back to sleep. You can dream about anything."

In his view, room temperature superconductivity is highly unlikely to be a thing of the past in their lifetime.

"I still have high hopes for that little guy. Even if he can't achieve room temperature superconductivity in the end, there's still hope for heat-resistant materials or heat-dissipating liquid metals."

Xu Guofu said seriously, "You may not have read his other paper. He discovered the thermoelectric material that was all the rage recently."

Song Yuntao was slightly taken aback. Of course he knew about thermoelectric materials, which was a very important matter for China, but he obviously didn't know about Chen Hui's relationship with thermoelectric materials.

However, he still sighed, "That's difficult too. I hope he succeeds!"

"But do you think it's possible for him, as a mathematician, to solve the problem of turbulence from a mathematical perspective?" Xu Guofu also entered a state of fantasy. Although he said this, he himself didn't really believe it.

Song Yuntao shook his head slightly. "Solving the turbulence problem is no simpler than synthesizing room-temperature superconductors, and may even be more difficult."

……

Upon returning to Yanbei University, Chen Hui immediately went to Zhihua Building, to Tian Yang's office.

"came back?"

Tian Yang glanced at the suitcase in Chen Hui's hand.

"I landed this morning and just got back from Mr. Qiu's place," Chen Hui told the truth.

Tian Yang nodded slightly. "I heard you've been studying the Navier-Stokes equations again recently?"

Clearly, Tian Yang already knew about what had just happened at Tsinghua University.

"Yes, I'm very interested."

Tian Yang nodded again, "You're still young. If you're interested in something, just go for it. Don't be afraid of making mistakes. You have enough experience to learn from them!"

He was naturally aware of the invitation from the Luzhou Plasma Institute, and it was even he who facilitated this visit. Therefore, he was not surprised that Chen Hui would be interested in the Navier-Stokes equations. He even had a vague feeling that Chen Hui could solve this problem that had plagued the mathematical community for nearly two hundred years.

"However, many professors at Yanbei University are also quite knowledgeable about partial differential equations. Why go to such lengths to seek knowledge elsewhere?"

Tian Yang got back to the point, saying with an arrogant expression, "Compared to theoretical mathematics research, Tsinghua University is not even worthy of being compared with us!"

Chen Hui nodded immediately, "That's right, that's what Old Qiu said too, so I came to find you as soon as possible."

Tian Yang chuckled softly.

He knew, of course, that Qiu Chengwu would never say such a thing, but Chen Hui's attitude was really hard to be angry about.

After discussing the Navier-Stokes equations with Tian Yang, Chen Hui went to the Boya Hotel, which Yanbei University had arranged for him, to prepare for the upcoming report meeting.

(End of this chapter)