Black technology, starting from daily check-in

Amidst the discussions of all the mathematicians in the audience, Lin Yu organized his thoughts, came to the whiteboard, picked up a black marker, and then turned on the Ultrain without hesitation to write.

"Let v(x, t) be a three-dimensional vector field describing fluid velocity, and p(x, t) be fluid pressure, the Navier-Stokes equation is: αvαt+(v▽)v=—▽p+ vΔv+f(x,t).

Among them: v>0 is the dynamic viscosity; f(x, t) is the external force; ▽ is the gradient operator; Δ is the Laplacian operator.

The above equation is a vector equation, which can be decomposed into three scalar equations, and the velocity and external force can be decomposed into components under three coordinates:

v(x,t)=[u1(x,t),u2(x,t),u3(x,t)]

f(x,t)=[f1(x,t), f2(x,t), f3(x,t)]

Then the Navier-Stokes equation can be written in the following form...

.........

When Lin Yu first started to solve the problem, everyone present didn't think so.

Because Lin Yu's problem-solving ideas are very general, and he uses the sieve method commonly used by all mathematicians to deduce.

In the entire mathematics world, countless mathematicians use this common method to deduce the NS equation every day, but no one can successfully push it to the end.

Because the various mathematical formulas and various calculations that need to be used in this are really amazing.

Even Deligne, the well-known top mathematicians in the mathematics world, chose to put aside this worldwide problem that cannot be solved by manpower.

Therefore, they prefer to spend time and energy on other world-wide problems rather than conquering such a world-wide problem that is impossible to prove mathematically.

Because it is better to study the other world's seven millennium problems than to study the Navier-Stokes equation.

After all, except for the Navier-Stokes equation and P and NP problems, the other seven millennium problems in the world can basically make progress.

Even if this progress is not of any substantive use for solving the problem.

However, as long as someone conquers and finds a problem, sooner or later there will be progress in solving the problem.

As time goes by.

However, when everyone took it for granted that Lin Yu would also fall into the sand, they immediately widened their eyes and stared straight at the whiteboard on the reporting platform.

"Old Chen, look at the sieve method used by that kid Lin Yu, it seems to be a little different from the sieve method commonly used in mathematics now?"

Sitting on the seat, old man Qiu Chengtong stared at the whiteboard on the reporting platform, and asked doubtfully without looking back.

"Indeed, the sieve method he uses now is different from any sieve method commonly used in mathematics."

Mr. Chen Shengshen nodded solemnly.

After pondering for a moment, Mr. Chen Shengshen seemed to have thought of a certain possibility, and said with uncontrollable excitement and trembling in his tone: "I can see it! His sieving method seems to be a brand new sieving method! A new sieve method that has never appeared in the mathematics world!!"

As we all know, there are three kinds of sieve methods most commonly used in mathematics.

The first is the O(n√n) violent sieve method (n≤2e5).

It can judge whether there are factors one by one, and then filter, which is the most commonly used method, and it is very convenient when the complexity is small.

The second type is the most classic O(nlog2n) Esperanto sieve (n≤1e6).

It can sieve out its multiples for each number, and it is divided into large sieve method, small sieve method and so on.

As for the third type, it is O(n) Euler sieve (n≤1e8)

These three sieve methods are very commonly used in mathematics. Generally, these three methods can solve most of the problems that need to be used in mathematics.

Of course, in addition to these, there are many special sieve methods that need to be used in a very small range, such as the Min_25 sieve method and so on.

It's just that the screening method Lin Yu uses now is not any of them!

"A brand new sieving method!?"

After listening to Mr. Chen Shengshen's words, Mr. Qiu Chengtong next to him was shocked.

He no longer cared about Lin Yu who was still solving problems on the stage, and subconsciously looked at Mr. Chen Shengshen next to him, with a shocked expression on his face.

The brand-new sieve method means more than just proving a conjecture!

It represents a revolution in mathematical tools!

It is no exaggeration to say that its appearance is enough to make countless unsolved mysteries in the mathematics world, and it is possible to solve the mysteries again!

With it, the development of the whole mathematics will take a big step forward!

Even Lin Yu's name and this brand-new screening method will be engraved in the history of mathematics!

And as long as Lin Yu is willing, the name of this new screening method will be named after his surname!

At this moment, it was not only the two old men who were shocked, but even Deligne, who was sitting in the front row, and other top figures in Princeton mathematics, were shocked by the new screening method displayed by Lin Yu on the report stage.

"Fal, have you seen it?" Deligne showed a bright smile on his face.

"Well, a brand new sieving method."

Faljens continued with a heavy tone: "I can see the shadow of re-sieving method and Essie's sieving method from this new sieving method. As for whether there are other sieving methods, I don't know, but at present It seems that the effect of this new screening method is very powerful."

"Because it almost combines the advantages of many sieve methods, and its most powerful thing is that the disadvantages of those comprehensive sieve methods are all abandoned, without even the slightest disadvantage. It is so perfect that it is not like Humans can achieve."

At the end of the speech, Faljens shook his head with admiration, and looked at Lin Yu on the report stage with a complicated expression.

To be honest, he has been in the mathematics world for so many years, this is the first time he has seen someone with such perverted abilities.

The abnormality almost refreshed his definition and cognition of genius.

"Faljens is right, this new sieve is just perfect."

Just after Faljens' voice fell, Andrew Wiles next to him also sighed and said: "Actually, I once thought of synthesizing the advantages of the sieve method in the mathematics world like Lin Yu, but its The difficulty is really too great, even if I tried tens of thousands of deduction, I can only make a rough synthesis of the heavy sieve method and the large sieve method in the Escherbeck sieve method.”

Speaking of this, Andrew Wiles couldn't help but glanced at Lin Yu on the report stage with admiration, and then continued with a wry smile: "The combination of the advantages of my rough two screening methods is the same as what Lin Yu is expressing now. Compared with the new sieving method, it is almost like the carriage of the 17th century and the current high-speed rail, the gap between the two is really too big..."

After all, Andrew Wiles sighed helplessly.

And after listening to the words of the two, the eyes of many top mathematics experts around them also flashed complicated lights.

There are surprises and envy, but more appreciation and admiration for the younger generation.

"As long as Lin Yu can successfully find a weak solution to the Navier-Stokes equation, then this year's Crawford Award must belong to him."

"Not to mention the Crowder Award, just this brand-new screening method alone is enough to nominate Wolfe and Fields!"

"If only he could stay in Princeton, working with this kind of young man who is never short of inspiration, just thinking about it is full of energy..."

"Hehe, that's probably impossible. I heard from Deligne that this young man loves his wife very much. Even when Deligne personally invited him, he politely declined without hesitation."

"Oh, what a pity..."

At the time when many top mathematics experts in the front row were discussing lively while watching Lin Yu's problem-solving process on the stage.

The other mathematicians in the reporting hall were not so relaxed.

The reason is very simple. They only saw Lin Yu writing vigorously on the whiteboard, but they didn't understand the proof process written by Lin Yu with a new screening method.

"Hey, Jack, do you understand?"

On the seat behind, a young man with blond hair and blue eyes patted on the side wearing gold-rimmed glasses, and stared blankly at one of the blond men on the whiteboard of the report desk.

The blond man called Jack didn't seem to sense the behavior of his companion.

After a long time, his pensive face relaxed, and he shouted excitedly: "I understand! I understand!!"

However, after a while, he looked at the calculation formula on the notebook on his knee with a sad face, and muttered to himself: "But I really think I made a mistake..."

After seeing this scene, the companion next to him couldn't help shaking his head helplessly, and immediately continued to work hard to study the calculations on the whiteboard.

Such a scene can be seen everywhere in the lecture hall. Many young people are dejectedly solving a formula written by Lin Yu.

Even some old professors were stumped by some of the formulas.

They were all wearing reading glasses, and they were constantly deducing in their notebooks, while searching for information from the Internet.

For a while, as more and more writing sounds sounded, most of the people in the entire report hall fell into a state of flow with focused expressions.

Sometimes they are ecstatic, sometimes dejected, and sometimes solemn.

As the time passed by every minute and every second, there were more and more calculations on the whiteboard.

Soon, the special five-meter-long whiteboard on the reporting platform was completely filled by Lin Yu.

And as early as when Lin Yu was about to finish writing, the staff not far away quickly moved up a five-meter-long whiteboard.

Therefore, Lin Yu didn't stop at all, he continued to write quickly on another whiteboard.

"In summary, the momentum equations in the three directions of x, y, and z can be obtained:

α(pv·x)αt+α(pv·x, pv·x)αx+α(pv·y, pv·x)+α(pv·z, pv·x)＝fx(αoxxαx+αTyxαy+αTzxαz) ...

—————(10)

Obviously, the number of the above equations is less than the number of unknowns, the equations are not closed, there is no solution, and other equations need to be introduced to make the equations closed.

Therefore, the following constitutive equations are introduced on the basis of the above equations, that is, the relationship between stress and velocity is established.

αxx＝-p+2u·αvxαx-23u(αvxαx+αvyαy+αvzαz)

αyy=-p+2u·αvyαy-23u(αvxαx+αvyαy+αvzαz)

αzz=-p+2u·αvzαz-23u(αvxαx+αvyαy+αvzαz)……

—————(11)

Then, by combining equations (10) and (11), the complete form, constant viscosity NS equation vector form can be obtained...

……

Fifty lines, eighty lines, 120 lines...

In the state of Lin Yu's full firepower, in less than 10 minutes, the space on this five-meter-long new whiteboard bottomed out again.

Helpless, the staff had no choice but to continue to work on the whiteboard.

With Lin Yu's crazy writing, when he was writing about line 150, Deligne and the others in the front row, the top math masters, finally started to struggle.

The next moment, they took out the notebooks they had prepared long ago, put them on the table, and began to deduce them seriously.

And as they also carried out deduction, in an instant, the entire lecture hall where mathematicians gathered suddenly became quiet, only the clear sound of writing sounded continuously.

For a moment, everyone seemed to be back in their school days, all lowered their heads, and calculated seriously.

Faced with this familiar situation, many staff members became cautious, afraid of disturbing everyone.

"Old Chen, do you think he can succeed?"

On the seat, Mr. Qiu Chengtong had already given up the deduction. He stared at Lin Yu who was writing hard on the podium, and whispered to Mr. Chen Shengshen next to him.

Hearing this, Mr. Chen Shengshen thought carefully, then nodded slowly, and said seriously: "If even he can't figure it out, then I can only say that it must be a problem with this topic."

As to whether Lin Yu could prove the Navier-Stokes equation, Mr. Chen Shiingshen was sure.

Because since Lin Yu has successfully proved the Riemann conjecture, which is one of the world's seven major millennium problems, it is impossible for the Navier-Stokes equation to prove unsuccessful!

Although the duration of this process may be a little longer.

However, Mr. Chen Shengshen always firmly believed that Lin Yu would prove his success.

Time passed slowly in this quiet atmosphere.

As more and more people gave up the deduction, everyone's hearts began to become tense.

Although most of the people present were confused, they couldn't tell whether Lin Yu's proof was correct or not.

However, Lin Yu's ability to write down these hundreds of lines of calculations is already amazing enough.

an hour and a half later...

Just as Lin Yu was writing on the No.11 five-meter-long whiteboard, the person in charge of the logistics of the report ran to Deligne who was deducing anxiously: "Professor Deligne, our special whiteboards are all After finishing writing, the ordinary whiteboards are also being dispatched urgently, but it will take some time to reach the report hall,"

His thoughts were interrupted, Deligne quickly came back to his senses, and asked with a serious expression: "Then do we have any other ordinary blackboards or ordinary whiteboards?"

"The lecture hall is gone, but there should be Princeton classrooms and the Princeton corridor." The person in charge said truthfully.

"Okay, then you arrange for someone to bring me all the free whiteboards and blackboards in Princeton University!"

"No matter what happens today, the verification process of the Navier-Stokes equation must not be interrupted, because this scene will be enough to be recorded in the annals of the mathematics world!" Lin Yu said firmly.

"understand!"

The person in charge had a serious look on his face, and immediately took out the walkie-talkie and ran outside quickly.