Soon after, the tea was brewed.
A thick mist floated around the teapot.
The old man picked up the teacup and took a sip. After moistening his throat, he slowly spoke.
"Out of the many partial differential equations, the Navier-Stokes equation is probably the most difficult one. Other than a few specific problems, we can't directly solve the partial differential equations constructed by the Navier-Stokes equation. We can only try to find an approximate solution.
"As for the turbulence phenomenon, as far as I know, the Clay Institute has been researching it, and they have invested a lot of money into it. However, even though there have been some results, they aren't big results.
"As for the plasma turbulence, I think it's even more difficult. First of all, computers can't handle calculations of that magnitude, so we can only do approximate solutions. Second of all, we don't have accurate observation data, so we can only rely on inaccurate diagnostic data. "
Lu Zhou: "Why?"
Old Qiu smiled and said, "Because we don't have an effective observation method for high-temperature plasma. For example, if we take a nano-scale probe and poke it into a gas to collect data on the gas molecules, we can basically ignore the disturbance of the probe itself.
"But high-temperature plasma is different. We can use electrostatic probes and magnetic probes for mild plasma, but for high-temperature plasma, any small disturbance can cause the entire system to collapse. The end result is that the electromagnetic field can no longer restrain the plasma, and the plasma will directly hit the first wall.
"Therefore, we can only use the electromagnetic waves emitted by the plasma to obtain relevant plasma parameters, which can then be used to establish a phenomenological model. However, because the electromagnetic wave spectrum emitted by the plasma is very wide, the information contained in it is quite messy. Therefore, the established phenomenological model is only accurate within a limited range. "
Lu Zhou asked thoughtfully, "Is there a way to solve this?"
"No, this is a technical ceiling." Old Qiu put down the teacup and shook his head. He then said in a joking tone, "If you can design an experiment to observe high-temperature plasma, your contribution to plasma physics will be no less than the contribution of cryo-electron microscopy to biology."
Lu Zhou had a helpless smile on his face.
Even though the system included engineering, a person's energy was limited. Lu Zhou had never delved into this field. Even though he received an increase in talent, it didn't give him a better understanding.
He might be able to design the experiment.
However, it was beyond his ability to design experimental equipment.
"My personal suggestion is that since the experimental tools can't be solved yet, why not try to improve the theoretical tools first?" The old man paused for a second and looked at Lu Zhou with a puzzled expression. "Logically speaking, mathematics is your strength, right?"
The moment he heard this, Lu Zhou was slightly stunned, and a trace of understanding suddenly arose in his heart.
That was right.
Mathematics was his forte.
Since the experimental tools could not solve the problem, why not perfect the theoretical tools first?
For example, he could research the Navier – Stokes equation itself. While researching the Navier – Stokes equation, he could improve the related theoretical tools. Just like when he was researching additive number theory, if he didn't have the previous series of mathematical propositions as a foundation, he would not be able to solve the Goldbach's conjecture.
Thinking of this, Lu Zhou's thoughts gradually became clear.
For the rest of the time, the questions that the two talked about were mostly in the field of mathematics.
Old Qiu had his own insights in the field of partial differential calculus.
Although the Navier – Stokes equation was not his research direction, he still had his own insights on this well-known partial differential calculus problem. These insights were of great help to Lu Zhou.
Just like that, time ticked by, and the clock on the wall had unknowingly gone through two rounds.
The steam on the tea table had long dissipated, and the tea in the cup was cold.
He didn't know how many cups of tea it had been, but Zhao Wei, who was sitting next to him, was restlessly fidgeting.
As a PhD student, he couldn't even say a word as he listened to the two professors talking about mathematics. He wanted to leave, but he was too embarrassed.
Lu Zhou had to admit that this was a painful thing to do.
Moreover, this pain did not only come from the mind, but also from the body.
Just now, in order to hide his embarrassment and ignorance by drinking tea, he accidentally drank a little too much …
On the third hour, the conversation between the two finally ended.
After Lu Zhou said goodbye to Old Qiu, Zhao Wei was finally free.
When Zhao Wei went downstairs, he quickly ran into the toilet and caught up to Lu Zhou.
"Boss, what did you guys just talk about?"
Lu Zhou was in a good mood, and he said, "We talked about some interesting things."
Zhao Wei rolled his eyes and said, "I heard about controllable nuclear fusion, that thing … Is it real?"
If it was real, then it would be too shocking.
Lu Zhou didn't answer the question. Instead, he asked, "What do you mean by 'real'?"
Zhao Wei paused for a second and said, "It's the kind that can be realized."
Lu Zhou smiled and said, "The meaning of science is to use scientific methods to realize things that can't be realized. Is there a need to research problems that have already been solved? Just go through literature. You're already a PhD student, why are you still asking these kinds of questions? "
Zhao Wei's face turned red as he scratched his head and smiled awkwardly.
"Boss, I want to buy you dinner, do you have time?"
Lu Zhou nodded and said, "Okay then."
It was almost time for dinner.
If someone bought him dinner, he wouldn't refuse.
…
After talking with Old Qiu, Lu Zhou was inspired.
Like Old Qiu said, before solving the problem, it was more important to create the tools to solve the problem. Compared to the former, the latter was the key to the problem.
Basically, before he could climb over the wall, he needed to build a ladder for himself.
What he had been doing before this was like circling around an insurmountable wall.
After finishing his trip to Harvard, Lu Zhou returned to his Princeton room. He had a new research idea, and he felt like every cell in his body was filled with endless inspiration.
Lu Zhou couldn't wait to sit in his study room. He looked at the new piece of paper and twirled the pen in his hand as he muttered to himself.
"… Building a theoretical model for plasma or a more accurate phenomenological model requires more accurate observation data, not diagnostic data.
"Since I can't solve the problem with experimental tools, I'll start with something I can solve!"
Lu Zhou gently stretched his neck and picked up the pen. He then wrote a title on the blank paper.
[Research on the global existence of smooth solutions for three-dimensional incompressible Navier-Stokes equations at specific initial values.]
He looked at the title and was full of energy.
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