Summarize the Navier-Stokes equation in one sentence, which is used to explain fluid motion.

From the movement of airplanes and ships to the way blood flows through veins and arteries, fluid movement is everywhere.

After the death of Navier and Stokes, the N-S equation continued to be studied and important progress was made.

There is only one problem left, and the most fundamental one: no one can find a formula to solve the N-S equation.

To be precise, no one can prove in principle whether the N-S equation has a solution or not.

The stubbornness of scientists lies in the search for the truth, and human beings have developed many theories, manufactured various tools, and applied them to various engineering scenarios in the past one or two centuries with an equation that is unknown whether it has a solution or not.

Scientists always feel a little panicked in their hearts, especially scientists like Shen Qi and Witten, who have far-reaching considerations.

A conference room in the center.

Zhou Yu'an said: "Fluid motion satisfies the conservation of mass, linear momentum, and angular momentum, and the result is that six additional motion characterization quantities must be introduced, which are three independent components of Reynolds stress, two dynamic viscosity and one independent component of dynamic pressure. ”

"However, I think there is a problem here, satisfying the three conservation laws while negating the N-S equation, and the choice of Reynolds stress has the dynamic viscosity and dynamic pressure, which means that there are 6 free quantities to choose from! "Zhou Yu'an has his thoughts, he states his thoughts.

Xiao Junlong continued: "Lao Zhou, this problem is a fatal internal injury of fluid mechanics, the original derivation of the N-S equation only requires the conservation of linear momentum and angular momentum, and the fundamental reason for adding the conservation of mass is that the conservation of angular momentum cannot be characterized. You and I must have understood the two mechanical perspectives of the N-S equation when we were Ph.D., first, conservation of mass + conservation of linear momentum. Second, conservation of linear momentum + conservation of angular momentum. ”

The first point of view introduces the concept of matter velocity and Euler velocity, so as to maintain the basic pattern of finding the three velocity field components of three equations, which is the current popular theory of fluid mechanics. However, I regret to find that the N-S equation is unsolvable based on the first mainstream theoretical system. Zhou Yu'an shook his head, his expression incomprehensible.

"You're so right, Lao Zhou, the hero sees the same thing!" The collision of ideological sparks produced a friendship of steady progress, and Xiao Junlong was also very puzzled: "The second point of view is also problematic, it introduces the vorticity vector, but it still maintains 3 equations to find 3 velocity field components, so this is very contradictory, at this time the velocity is not commutable to the derivative of spatial coordinates! Although some people have introduced the Lie algebra form, the engineering value is not great, because the theoretical basic concept is confused. ”

"So, the N-S equation is unsolvable?" Zhou Yu'an and Xiao Junlong summed up and deduced such a conclusion.

Shen Qi and Witten, who had been listening, smiled and didn't speak.

In order to make Witten understand, the conversation between Zhou Yuan and Xiao Junlong just now was in English.

Through intense and rigorous inference, exchanges, and discussions, the two deputy leaders, Zhou and Xiao, both believed that there was no solution to the N-S equation.

In fact, this is also the current situation in academia.

Engineers are always able to introduce additional conditions to the equations for specific problems, so that the N-S equations have a solution.

However, the results obtained are correct for their specific problems, but not of general significance.

This is why the vast majority of scholars believe that there is no general solution to the N-S equation.

Finding this golden key, or giving convincing evidence to prove that this golden key does not exist at all, is an operation with scientific value.

Zhou Yu'an and Xiao Junlong glanced at each other, shook their heads and smiled.

It's still too naïve, and the 10 million dollar project will definitely be beaten up if it is handed over like this.

Zhou Yu'an and Xiao Junlong looked at Shen Qi and Witten.

According to the conventional script design, after the debatable lines of the red-faced supporting characters are finished, the calm and calm protagonist should come forward next, give a decisive and correct answer, and lead the team to a broad road.

"Edward, you speak first. Shen Qi said to Witten.

"It's not a system problem, it's an algorithm problem. Witten said calmly and calmly.

Shen Qi, Zhou Yu'an, Xiao Junlong: "Hmm. ”

Witten walked over to the water dispenser and took a paper cup, which he placed under the spout and pressed the water dispenser.

The water jet drains down at a fixed flow rate and flows into the paper cup.

After the paper cup is filled with pure water, the water overflows, and it is booming.

"This is the first experiment. Witten handed Zhou Yu'an a paper cup full of water and said, "Zhou, drink it." ”

Knock knock knock.

Zhou Yu'an drank all the water in the cup, this cup of water has no sweet or salty taste, it is the original taste of ordinary bottled pure water.

Witten took the empty cup in Zhou Yu'an's hand and came to the water dispenser again.

This time, Witten pinched the paper cup, but it was not completely deflated, but half-deflated.

Bang la blah.

Under the operation of Witten, the water dispenser outlet flows out of the water column at a small water flow rate and leaks into the half-deflated paper cup.

Because Witten exerts an external force on the paper cup, the paper cup does not expand to its original shape under the condition of continuous filling with water.

Witten maintains the external force exerted on the paper cup to maintain the irregular shape of the paper cup holding water.

"This is the second experiment. Witten walked up to Xiao Junlong, made a water-feeding gesture, and said, "Xiao, drink it." ”

"But...... Zhou just used this paper cup!" "Although Xiao Junlong is not handsome, he is a man who loves cleanliness and hygiene.

"Don't worry about these details. Witten said.

"Okay, Edward, I'll drink. Xiao Junlong glanced at Zhou Yu'an and asked in Chinese: "Old Zhou, you shouldn't have hepatitis, right?"

"Look at your appearance, what kind of scientific research are you doing?" Zhou Yu'an forcibly held back his laughter.

Xiao Junlong's eyes closed, his heart was horizontal, and he drank the water in the cup under the service of Witten.

Witten said: "Through two experiments, we found that under the same water dispenser system, the same paper cup is less loaded with water than the first time because of different additional conditions. ”

Zhou Yu'an, Xiao Junlong: "Hmm. ”

Shen Qi smiled, no uh-huh.

Witten likes to use simple props at his fingertips to demonstrate and illustrate some profound scientific principles: "As you mentioned earlier, engineers are always able to introduce additional conditions to specific problems so that the N-S equation can be solved. However, these additional conditions are deliberate, and even if the solution of the N-S equation is solved, it can only meet the specific situation that they originally set, and it is not universal. ”

"There is a significant difference in the amount of water charged twice in the same paper cup due to different additional conditions. But it is undeniable that they all worked as an engineer, and they solved Zhou and Xiao's thirst problem. Therefore, I believe that the fundamental problem with the N-S equation is not a system problem, but an algorithm problem. ”

Witten came to the water dispenser and restored the paper cup in his hand to its original state: "Who can design a third experiment next, which is also based on this water dispenser system and gets a universal solution?"