When I am reborn, I just want to be a top student

"Regarding the derivation of the continuity equation, I personally think that the more natural way to derive it is to use the conservation of matter described by Euler and the body derivatives."

"Consider the change in density in a region Ω in space. Since the region we choose does not change with time, that is, we use Euler description, then physics is differential with respect to time and does not contain volume terms. In other words, these physical quantities are regarded as functions of spatial coordinates, not functions of fluid particles."

"Then, due to the law of conservation of matter, the change in mass in the region is equal to the difference between the mass entering the boundary and the mass leaving it, so that..."

As Wang Donglai spoke, he wrote down the formula he derived on the writing board.

At this moment, everyone in the audience looked very focused and dared not blink, for fear of missing the crucial moment.

After all, this is the NS equation!
It is much more important than other difficult math problems.

"Using Gauss's formula on the right side of the equation and taking into account the arbitrariness of the integral region, the integral is formalized into differential form..."

"This is the textual differential form of the continuity equation. Considering the relationship between the body derivative and the non-body derivative, the continuity equation can be transformed into... The definition of an incompressible fluid is... Therefore, for an incompressible fluid, the continuity equation becomes..."

"Notice!"

Wang Donglai tapped the writing board lightly, and a buzzing sound came from the microphone, attracting everyone's attention.

"The dp/dt here refers to a given fluid particle, that is, for a certain particle, its density does not change with time, but it does not mean that the density of different particles is equal. In fact, if this condition is also added, the fluid density field is constant at any time in the entire space."

"..."

"Considering the Lagrangian description of the velocity field and density field, we still select a region Ω. Since the Lagrangian description is used, this region can be regarded as a fluid micro-group that changes with time. At this time, we need to consider the body derivative of the material integral."

"According to the momentum theorem, the change in momentum of a fluid particle per unit time should be equal to the sum of the body force impulse received by the fluid particle throughout the interior and the surface force impulse at the boundary."

"..."

"When constructing the energy equation, we still have to use the Lagrangian description. According to the law of conservation of energy, the total energy change of the material micro-group Ω is equal to the sum of the work done by the outside world and the heat transfer."

"Note that in the more general case, the heat transfer rate k is a second-order tensor and can be considered a scalar only under isotropic conditions..."

There is generally a rule in academia.

That is, there is a certain correlation between academic research ability and physical fitness.

People with good physical fitness may not necessarily have strong academic research abilities, but if you want to achieve academic results, a strong and sturdy body is necessary.

Just like this moment.

The proof of the NS equation cannot be explained in just a few words.

Or Wang Donglai could just come up with a formula and say that this is the proof.

This is simply impossible.

In addition, Wang Donglai also needs to make the proof process as easy to understand as possible to avoid the scholars present being unable to understand it because it is too complicated.

As a result, the proof process naturally becomes extremely cumbersome.

However, even though Wang Donglai had tried his best to make it simple, it was still beyond the acceptance of many scholars present.

In less than half an hour, nearly a hundred scholars had fallen behind and could not keep up with Wang Donglai's thinking.

At this time, the gap can be clearly seen.

The majority of scholars who fell behind first were professors from domestic universities.

It is inevitable to deal with human relationships.

This academic exchange meeting was held at Tangdu Jiaotong University, and the theme was proposed by Wang Donglai.

China is naturally the undisputed organizer, and Tangdu Jiaotong University also has the quota to attend the conference.

This conference venue was specially renovated by Tangdu Jiaotong University.

Tangdu Jiaotong University came up with this idea when Wang Donglai came to defend his graduation thesis.

Sure enough, it was used within two years.

The super conference hall that can accommodate thousands of people can no longer be called an academic exchange conference, it can be said to be a mathematicians' conference.

Among the scholars who came next, there were not many from overseas, accounting for only about one-fifth of the total number.

The remaining places were given by Tangdu Jiaotong University to major domestic universities and research institutes.

Wang Donglai also understood this matter and did not refuse.

In fact, reserving a large number of places for domestic scholars and enthusiasts is what he wants to do.

If China's mathematics profession wants to develop, it cannot rely on one person alone.

Even Wang Donglai, on his own, has pushed mathematics to a new height.

But if there is no successor to inherit this knowledge, it will be like a castle in the air, without any foundation, and will collapse at the slightest disturbance.

Wang Donglai would naturally not do such a thing, let alone allow such a thing to happen.

However, he understood more clearly that mathematics really depends on talent.

If it works, it works. If it doesn't, it doesn't work.

There is almost no scholar without talent who can make any major scientific discoveries after hard study and research.

Half an hour passed!

An hour passed!
Wang Donglai has already filled three writing boards with various mathematical symbols.

Just like English.

Looking around, there are not many scholars who can follow Wang Donglai's ideas and persist until this time.

Regardless of whether scholars can follow Wang Donglai's thinking or not, their actions are similar at this moment.

Either he was recording important points with a pen, or he was checking calculations on a piece of scratch paper.

Even though Wang Donglai deliberately slowed down the process and performed detailed analysis on some links, the NS equation was still too difficult.

Therefore, many scholars simply cannot keep up with the pace.

I could only verify and prove little by little the parts where I couldn't keep up with the pace, and try to continue thinking along Wang Donglai's line of thought.

But the situation is different for top mathematicians like Terence Tao, Deligne, and Cheng-Tung Yau.

The more they listened to Wang Donglai's story, the brighter their eyes became.

The reason why a few people can become the world's top mathematicians is because of their talent, diligence and persistence, and finally, their genuine love for mathematics.

All three are indispensable. Without any one of them, one cannot become a top mathematician.

Therefore, at this moment in the minds of the three people, based on the proof process and data that Wang Donglai has provided, they can preliminarily determine that Wang Donglai has proved the NS equation.

However, the three would not directly state their judgment until they had heard the final result and verified the result.

This has happened many times in mathematics.

Obviously all the steps were correct, but at the last step, a wrong result was obtained, which made all the previous work go to waste.

Deligne and others have seen many such things.

Therefore, no matter how confident he was in Wang Donglai, he would not show it obviously, and would not express his opinion before the results came out.

Some people were scratching their heads, some were frowning, some were looking happy, and of course, some had dark faces.

Those were the people who had caused trouble before.

Originally, according to Huang Yun's instructions, he was going to let the security personnel kick these people out directly.

But since Wang Donglai said that, Huang Yun naturally gave up this idea and let a few people stay.

The few people who were able to sneak in must have some abilities.

With anger towards Wang Donglai in his heart, he pricked up his ears and listened attentively when Wang Donglai was proving himself, trying to find problems in Wang Donglai's proof.

One million is not a small amount, but to them, it is nothing.

What they care more about is that as long as they can find a problem in Wang Donglai's proof process, they can use it to publicize that there is a problem with Wang Donglai's proof.

However, no matter how hard they tried, they couldn't find any problems, and their faces gradually became ugly.

"Can Wang Donglai really prove the NS equation?"

As soon as this thought emerged in the minds of several people, it was dismissed by them.

It’s not that they think it’s impossible, but that they simply don’t want to believe it and accept this fact, so they can only choose to paralyze themselves.

Time is still passing by little by little.

Two hours!

Three hours!

Even the scholars sitting below were finding it difficult to sit still.

It’s not that they can’t sit still, but the high-intensity thinking puts a heavy burden on the body.

In addition, most of the scholars are in their fifties. Even if there are some slightly younger ones, the average age is in the early fifties.

This age is no longer considered young, and three hours of non-stop intensive thinking has made many people feel that they can’t hold on any longer.

just.

Wang Donglai on the stage showed no intention of stopping.

When the writing board is full, it is hung up and replaced with a new one.

Tangdu Jiaotong University had been specifically reminded of this by Wang Donglai long before, so they were fully prepared.

It was impossible for everyone to leave early before Wang Donglai said the proof was over.

Since you have come to attend this academic exchange conference, you must persevere to the end.

"The governing equations of fluids in CFD can be expressed in a variety of mathematical forms, such as conservation and non-conservation. These expressions have common physical principles and can be converted into each other. However, when solving them using different numerical methods, choosing the right equation form can give a reasonable solution. Otherwise, problems such as non-physical solutions and instability may occur."

“Therefore, when learning the derivation of the basic equations of CFD, you must understand how these equations are derived, what their similarities are, what their differences are, how to convert between them, etc.”

“The derivation of fluid mechanics equations is first based on the continuum assumption, which ignores the distance between fluid molecules and regards the fluid as continuous and gapless, filling the entire space.”

"In addition, when a fluid is in motion, different parts of it can have different velocities and it is difficult for it to maintain a fixed shape, so to describe the motion of a fluid we need to select and appropriate model..."

"Using fluid microelement as the research object, differential equations will be derived."

"Using a finite control volume as the research object, we can derive an integral equation. The difference between the two is that the integral equation allows discontinuities in the control volume, while the differential equation requires the flow field variables to be continuously differentiable because it involves the concept of limit."

"The equations derived by Euler's method are conservation equations, while the equations derived by Lagrange's method are non-conservation equations."

"..."

"As a nonlinear partial differential equation, the NS equation has a very complex solution, with different solutions in different situations. It is difficult to describe it using current mathematical language."

"If I have to write it down, the analytical solution would probably be presented in the form of an infinite series."

"And in order to make it clearer for everyone to understand, I have simplified it a bit."

Wang Donglai didn't even turn his head. He wrote a long mathematical formula on the writing board and spoke calmly.

When people in the audience heard Wang Donglai say this, their expressions varied.

Wang Donglai's words were almost as good as calling them idiots.

If it were a different place, a different time, or someone else said something, everyone would definitely not be as calm as they are now.

However, the person who said this at this moment was Wang Donglai.

He is the world's top mathematician who is proving the NS equation!

As for their academic level, they had already realized it when Wang Donglai was explaining it.

So, what Wang Dong said was not wrong.

Their level is indeed not up to par.

Even the proof process that Wang Donglai had simplified was still quite difficult for them at this moment.

When everyone was thinking this in their hearts.

Wang Donglai also wrote down the final mathematical formula on the writing board.

"The above is my entire proof process."

Wang Donglai turned around, looking calmly at the thousands of scholars and professors in the audience, and spoke confidently.

Although there was only this one sentence, everyone present could understand that Wang Donglai had not said another sentence.

That is: "I have proved the NS equation, and now there is one less difficult math problem!"

After a few breaths.

Everyone in the venue stood up at the same time, stretched out their hands and clapped.

"Clap clap clap..."

The applause was like thunder and overwhelming.

Although it is still impossible to thoroughly verify whether there are any problems with Wang Donglai's proof and whether he has really proved the NS equation, what they have learned from Wang Donglai's proof is enough for them to applaud and express their gratitude.

The applause lasted for three full minutes.

The cameraman from the central station who stayed in the venue also captured some very impactful photos.

Amid the excitement, there was something a little out of place.

Those were the few people who had stood up to question Wang Donglai before, and their faces looked extremely ugly at this moment.

They could neither understand Wang Donglai's entire proof process nor find any problems in Wang Donglai's proof process.

Therefore, they dare not say whether this difficult mathematical problem has been proved.

"This proof process has not been verified yet, so it cannot be said that the NS equation has been proved!"

Soon, several people thought of this and shouted loudly.

This immediately attracted a lot of unfriendly looks. (End of this chapter)