Section 229

After calling his assistant in, Xiao Yi asked him to make an appointment with the relevant leaders and prepare to discuss the next expansion of the Science Island Laboratory with these leaders in a few days.

Wang Hao got the task and then left the office.

Xiao Yi brought a pile of draft paper from the side.

These scratch papers record his research on Greenwald's limit.

"Hmm... Judging from the calculation results, it seems that the limit has indeed been reached. However, such limits are determined based on the current fixed plasma flow trajectory."

"Could it be that the plasma flow can only move in this form?"

After groping his chin, Xiao Yi thought for a moment and wrote a few simple lines on the draft paper.

【ρ(v/t + v·v)=-p……】

[(ρε)/t+·(ρεv)=-·q-p·v+j·E+·(Π·v)……]

…

"For the fluids in the tokamak device, a multi-fluid model is generally needed. Such a model can accurately describe the complex processes of plasma, such as ionization, ionization, etc., such as the one mentioned by Director Zhao of the Institute of Plasma. paper, the drift-simplified Braginskii fluid model used in it is a multi-fluid model.”

"It's just that the multi-fluid model is a little inferior when it comes to turbulence and boundary layers. At the same time, there are also certain incompatibility issues in the coupling with the magnetic field process."

"On the contrary, the NS equation has sufficient advantages in this aspect."

"Hmm... maybe it would be a good choice to combine the two for research?"

Xiao Yi thought so in his heart.

I checked the relevant information online and found that there are indeed some models that combine NS equations with multi-fluid theory, such as the multi-fluid NS equation coupling model, the NS equation closure of the multi-fluid model, and the two-fluid NS equation model.

Then he searched for related research on these models, but there were no particularly outstanding results. As for whether they could help him solve this problem, it was even less likely.

But think about it too.

If other models were feasible, they would have been discovered by other scholars long ago.

"Well... in the end I have to give it a try myself."

Then, he started to take action.

【ρ(tu+uu)=p+μΔu+f……】

【ns/t+(ns·vs)=0】

【ms(tvs+vsvs)……】

…

In this way, time passed quickly.

An hour later.

Xiao Yi, who had been thinking uninterruptedly, suddenly frowned.

He encountered a problem.

The solution of the new model may suffer from singularities or instabilities.

According to his derivation, the energy of some local solutions may become infinite in a finite time. This phenomenon is called "explosion cracking", which means that the solution loses smoothness and appears singularity in a finite time.

In addition, when velocity shear is present, the solution may be unstable, causing the interface to fluctuate and gradually become chaotic, which is also called Kelvin-Helmholtz instability.

"This problem...should be caused by the NS equation."

He thought for a moment.

"And if you want to solve this problem, there is only one way... to prove the smoothness of the solution to the NS equation."

Xiao Yi fell silent.

This question is also known as one of the seven millennium problems.

It is also the last question of classical physics.

Existence and smoothness of solutions to NS equations.

So, is it possible that he wants to make dumplings for this dish of vinegar?

Chapter 206 Physically Transporting Hard Drives

Obviously, from the perspective of results, just raising Greenwald's limit is not that important compared to proving a seven-millennium problem.

After all, one is one of the most important core problems in the field of mathematics. It is also the last problem in classical physics. It has countless applications in reality. It can be used in any problem related to fluids. play a very important role.

The other is just a slightly important issue in the field of nuclear fusion. For nuclear fusion, what is more important are the major material issues. Only by solving these material issues can controllable nuclear fusion be realized. As for the Greenwald limit problem, it will have no significance until controllable nuclear fusion is officially realized.

Therefore, in order to solve a Greenwald limit problem and solve the smoothness problem of the NS equation, it can really be called making dumplings for a plate of vinegar.

"Um……"

Xiao Yi thought for a moment, and then thought: "Let's see if we can solve it in other ways first."

Then he temporarily put this issue aside and began to study how to combine the NS equation and the multi-fluid model from other perspectives.

In this way, time passed quietly for a long time.

It wasn't until it was almost night that he raised his head again and sighed helplessly.

"It looks like it won't work anymore."

For nearly half a day, he considered at least 4 methods, but they either didn't work, or the final model effect didn't reach the level he wanted, or they also showed singularity and instability.

Until the end, he turned his attention back to that problem.

The existence and smoothness of the solution of the NS equation.

"It seems that this roadblock really needs to be solved."

Director Zhao, Director Zhao, you really gave me a difficult problem.

Xiao Yi sighed slightly in his heart.

I guess Zhao Zhanyou didn't expect that the problem he asked Xiao Yi to help solve at that time would eventually lead to this top mathematical problem.

But no matter what, since he had promised to do it at the beginning, he had to give it a try.

Anyway, it's just a millennium problem.

It's not like he hasn't solved it before.

"It just so happens that I haven't studied mathematical problems for a long time."

Although most of the topics he solved before were using mathematical methods to solve various problems, he really hasn't studied such purely theoretical mathematical problems for a while.

"Come on!"

This is one of the seven problems of the millennium, the last problem in classical physics!

…

Xiao Yi's research on the existence and smoothness of the solution of the NS equation officially began.

The NS equation refers to the Navier-Stokes equation, named after French engineer and physicist Claude-Louis Navier and Irish physicist and mathematician George Stokes. It is a set of partial differential equations that describe the movement of fluids such as liquids and air.

The history of fluid research began more than 20 centuries ago, just like the story of Archimedes using buoyancy to measure gold that everyone has heard of. The Archimedes principle that was born from this can be regarded as the earliest scientific theorem of fluid mechanics.

Later, Da Vinci also observed fluids and made the earliest description of eddies and turbulence. Later, Newton, Euler, Bernoulli and other great men made more and more contributions to fluid mechanics.

Until the 19th century, Navier and Stokes summarized various previous studies on fluid mechanics and finally came up with the NS equation, the most important equation.

It can describe the conservation of momentum and mass in the process of various fluid motion, and use it to analyze the behavior of fluids in the process of flow.

It can be said that this equation is constantly playing a role in all walks of life.

From airplanes flying in the sky to pipeline design under the city, or submarines hundreds of meters under the sea, the NS equation is needed to analyze the fluid problems it brings.

As for why it is the last problem in classical physics, it is because other related problems in classical physics have been well solved. However, when using the NS equation to study fluid mechanics, since each fluid molecule in the fluid is completely free and can be affected by various other molecules around it, there are still places that people cannot analyze.

Especially at high Reynolds numbers, the fluid will become very complex and form turbulence, which is also one of the most complex phenomena in fluid mechanics, because its flow is highly random and irregular, just like a chaotic system, and its accurate description and understanding is still a huge challenge.

Unlike other classical mechanics problems, the complexity is not as complex as that in fluid mechanics, and basically they can be solved quite well, such as architectural engineering, etc.

Of course, just because the NS equation is difficult enough and has a very important position in the industrial field, there are quite a lot of people studying this problem. It can be said that it is a very important problem in the field of mathematical physics.

"However, the complexity of this problem is indeed quite high..."

As Xiao Yi began to study the NS equation, various difficulties followed.

The existence and smoothness of the solution of the NS equation are two problems.

Existence requires proof: for given initial conditions and boundary conditions, can we always find a solution that satisfies the Navier-Stokes equation?

And smoothness requires proof: Is the solution found smooth over the entire time range? That is, whether all derivatives of this solution exist and are continuous.

Of course, there is a more abnormal problem above this, that is, solving the NS equation.

As an equation, it can naturally be solved, but because the NS equation is too complicated, the possibility of obtaining its analytical solution is too great. The mathematical community generally believes that this is basically impossible to do, so the academic community basically only requires the existence and smoothness of its solution to be proved.

"For the NS equation in two dimensions, its global existence and smoothness have been proven, but for the three-dimensional case, only the existence of local smooth solutions has been proven, that is, the solution exists and is smooth within a finite time interval, but it has not been proven for the global case."

"When proving the global case, there will always be singularity problems."

Looking up relevant information about the NS equation, Xiao Yi analyzed the various problems encountered by the current academic community in the process of studying this issue.

Singularity is a problem he encountered when combining the NS equations and the multi-fluid model. It is mainly manifested in that the fluid velocity becomes infinite or its derivative becomes infinite in a finite time, just like a sudden explosion. Therefore, this problem is also called the explosion solution problem.