In Academician Jiang Weixian's laboratory, Qin Ke and Ning Qingyun had a very fulfilling and busy life. In the morning, they studied the existence of smooth solutions of N-S equations in three-dimensional space, and in the afternoon they worked on fluids in the "Turbulence Group"

Applied experiments in mechanics.

The S-level knowledge in Qin Ke's hand is the first, middle and last chapters of "Exploration and Detailed Explanation of Nonlinear Partial Differential Equations 'Navier-Stokes Equations'". It has very rich theoretical knowledge, including the conservation of mass of the N-S equation and the momentum theorem.

, Detailed explanation of energy conservation, the relationship between the N-S equation and Euler's method, the changes of the N-S equation in Newtonian fluids and incompressible fluids, etc.

In addition, there are variants such as the Euler equation and the boundary layer equation, as well as more than a thousand specific applications of special solutions - you must know that there are only more than a hundred special solutions published in the world - a total of more than 600 pages.

But there is no complete answer to the existence of smooth solutions to the N-S equations, and there is no clear proof process, let alone the so-called general solution of the equations.

It can be said that the first, middle and last chapters are more about the theoretical and application level exploration of N-S equations, which is enough to make Qin Ke, who is already good at fluid mechanics, become a top master, but he cannot directly obtain the Millennium Mathematics Conjecture.

Answer.

If Qin Ke guessed correctly, the answer to the question "the existence of smooth solutions to the N-S equations in three-dimensional space" and whether there is a general solution to the N-S equations can only be found in the final chapter.

This kind of knowledge arrangement has its rationality. First of all, no one can deny that the N-S equation is a combination of mathematics and physics. Only through the theoretical and applied knowledge in the first, middle and second chapters can we have a deeper understanding of the N-S equation itself.

For example, when will the N-S equation have a solution?

That is to introduce additional preconditions to the equation for specific application problems, so that the early variables of the N-S equation become quantitative one by one, and the nonlinear partial differential equation is transformed into a normal partial differential equation, and the solution can be naturally obtained.

And solve fluid mechanics problems under set conditions.

But this new problem will arise. The N-S equation can only have smooth solutions under specific circumstances, and there is no general solution in a general sense.

This means that if you want to use the N-S equation to solve specific fluid mechanics problems, you must obtain the special solution and its preconditions that others have obtained in advance; or you must study the N-S equation in depth yourself, set the preconditions, and find the special solution.

untie.

This kind of efficiency is undoubtedly inefficient, just like a handmade workshop can only rely on the craftsman's manual skills for production, which is prone to defects and errors, and cannot realize modern automatic production line operations.

It is undeniable that without practice and research in a manual workshop, it is impossible to evolve to an automatic production line all at once.

This is also the foundation and progressive role of the first, middle and last chapters of "Exploration and Detailed Solution of Nonlinear Partial Differential Equations 'Navier-Stokes Equations'".

Now Qin Ke has basically understood the mathematics part of the first, middle and last chapters. He can even use his "grandmaster level" mathematics level to spend time solving this millennium problem without having to wait for the mathematics in the final chapter.

part.

Only the physics part, because he only has a "professional level" physics level, still has 20 to 30% not fully understood. However, as he mastered more and more experimental methods and skills in the "Turbulence Group", he continued to learn more and more.

By transforming theoretical knowledge into practice, these physical theories that cannot be fully understood will all be overcome sooner or later.

All the research and application materials related to N-S equations of the research group that I have reviewed in the past ten years have been of great help to Qin Ke. Not only did he increase his academic points in physics by more than 100 points, but also deepened Qin Ke's understanding of the N-S equation.

Understanding the physical parts of the first, middle and last chapters of "Exploration and Detailed Explanation of Nonlinear Partial Differential Equations 'Navier-Stokes Equations'".

For Ning Qingyun, it is even more important. Ninety-nine percent of her knowledge about fluid mechanics comes from self-study in textbooks and Qin Ke’s teaching through "thinking resonance". She read most of the materials carefully this time - Ning Qingyun

Later, she often went to the reference room to continue reading the information - which greatly enriched Ning Qingyun's vision and deepened her understanding and application of the N-S equation.

Especially for the current task undertaken by the "Turbulence Group" - "Improving the aerodynamic characteristics of near-space vehicles in hypersonic thin air", deputy director Academician Guo Weiyang directly asked Qin Ke and Ning Qingyun to take charge of the most important mathematical modeling and experiments

Program writing work is an extremely rare opportunity for exercise.

In general, the two are currently jointly launching an attack on the existence of smooth solutions to N-S equations in three-dimensional space. The progress is not fast, but the progress is steady and steady. Mathematics and physics are advancing simultaneously, and both of them are fully devoted to it.

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Once this millennium problem is solved, their understanding and application of the N-S equation will surpass that of most mathematicians and physicists in the world.

…

Snowflakes had started to fall outside the window at some point, and the snow in the sky meant that the late winter of December was approaching quietly.

And as Christmas Eve approaches, Qin Ke's twenty-first birthday is also approaching.

Looking back on the past year, Qin Ke himself is very impressed.

At the age of 20, he proved Goldbach's Hypothesis and Riemann's Hypothesis, and won international awards including the Crafford Prize, Ramanujan Medal, and Fields Medal, in addition to a number of domestic awards.

Awards big and small can be said to be full of rewards.

What makes him most proud is not his academic achievements, but that the love between him and his little cabbage Ning Qingyun has not been diluted by the years, or has lost its freshness and turned into a family relationship.

On the contrary, she and Ning Qingyun have worked hand in hand and gotten along with each other over the years, making the relationship between the two like mellow wine, getting stronger with time.

"It seems like we need to plan carefully for Christmas Eve this year." Qin Ke touched his chin, thinking about Christmas Eve three days later.

On Christmas Eve and birthday last year, because of the accident involving senior Chen Licheng, both of them only focused on seeking justice for senior Chen and did not celebrate in particular. Even Qin Ke's birthday was made up as an afterthought.

This chapter is not finished yet, please click on the next page to continue reading the exciting content! This year Christmas Eve falls on a Saturday, so Qin Ke decided to celebrate it well.

But just after he asked his assistant Fang Yongtang to arrange the event, an accident happened. Ning Qingyun had a cold and fever the day before.

At that time, Ning Qingyun was reading a piece of information in the data room. Qin Ke was not with Ning Qingyun because he was called by the deputy director, Academician Guo Weiyang, to inquire about some details about the N-S equation.

When Qin Ke went to look for Ning Qingyun after finishing his work, he saw Ning Qingyun rubbing his forehead and couldn't help asking: "What, are you tired?"

Ning Qingyun turned around, and Qin Ke immediately saw that the girl's face was flushed with an unnatural blush, and her eyes were as blurry as mist.

Qin Ke's heart beat nervously. He went over and touched Ning Qingyun's forehead. It was very hot, and he obviously had a high fever.

Qin Ke felt distressed and panicked. You must know that Ning Qingyun's physical condition has greatly improved since practicing the Eastern Secret Code, and her resistance to viruses has been significantly improved. She has almost never been sick in the past three years.

I actually developed a high fever!

And looking at Ning Qingyun's appearance, he probably didn't have a sudden fever, but had been having it for a while, and he didn't even notice it!

Qin Ke couldn't help but secretly blame himself. Recently, his mind was either on N-S equations, quantum calculations and extreme weather data analysis, or he was thinking about planning activities to surprise Ning Qingyun, but he ignored the abnormality of the girl around him.

"You have a high fever. Let's go. I'll take you to the infirmary." Qin Ke couldn't help but pick up Ning Qingyun.

"Qin Xiaoke..." Ning Qingyun felt that her body was cold and hot, her hands and feet had no strength, and her brain was dizzy and uncomfortable. However, looking at Qin Ke's anxious, distressed and worried look, her heart couldn't help but change.

Warmly:

"I'm fine... Maybe my mother called me right after I washed my hair last night. I only blew my hair after I finished the phone call. I caught a cold. I had a fever when I woke up in the morning. I took medicine and it was fine. I thought it was just fine.

Well, I didn’t expect the fever to continue again in the afternoon..."

"Why didn't you tell me that you were sick..." Qin Ke saw the weak look on the girl's delicate eyebrows, and only half of the reproachful words disappeared without a trace, leaving only worry and distress: "Do you feel uncomfortable now?"

"I just have a little headache, dizziness and fatigue..."

Qin Ke didn't dare to delay any longer. He quickly took out his mobile phone and dialed Chen Ming's number: "Brother Ming, drive right downstairs to the laboratory building and wait for me."

After returning to school, someone else secretly protected Qin Ke and Ning Qingyun. Chen Ming and Chen Lan usually waited outside the school, and then quietly followed them when they left school.

Qin Ke became anxious at this time, and he didn't know the other person's phone number, so he called Chen Ming directly.

Chen Ming's voice tightened: "Wait, we'll be there in two minutes!"

Qin Ke put away his mobile phone, picked up the small schoolbag that Ning Qingyun placed next to him, took out the scarf inside and tied it for the girl, then put his down jacket on her, then picked up Ning Qingyun and walked out quickly

Data room.

Fortunately, Ning Qingyun usually wears pants in school, so she doesn't have to worry about being exposed when she is held horizontally.

The members of the research team were shocked when they saw this: "What's wrong with junior Qingjun?"

"Qingjun has a fever. I need to take half a day off. Please help me tell Academician Guo." Qin Ke didn't have the time to explain, so he hugged Ning Qingjun and ran out.

Taking the elevator of the laboratory building to the first floor, it was snowing outside, with white snowflakes covering the entire sky and earth, and the north wind whistling by, taking away the heat in the air.

The temperature is probably only 5 or 6 degrees below zero, and there are not many pedestrians on the school road.

Qin Ke hugged the girl in his arms tightly, and felt extremely distressed when he saw her little face that was burning red: "It's okay, we'll be at the infirmary soon."

"Well...I'm fine, don't worry..."

Qin Ke smiled at the girl, but he became increasingly anxious. In such bad weather, could Chen Ming arrive in two minutes?

Fortunately, there was heating on the first floor of the experimental building. When the security guard saw this, he came over and wanted to help. Qin Ke shook his head and declined.

At this moment, the car lights came on in the wind and snow, followed by a sudden brake. Chen Ming's car broke through the wind and snow, swerved, and stopped accurately at the gate. As expected of a special service agent, his driving skills are quite strong.

Normally, Qin Ke would definitely make a joke with Chen Ming, but he didn't care at this time. He hugged Ning Qingyun and rushed out of the building. Chen Lan, who was sitting in the passenger seat, had already pushed the door open. Seeing this, his face changed and he helped

Then open the rear seat door.

Qin Ke quickly sat in: "Go to the school's infirmary!"

Chen Ming said nothing. When Chen Lan jumped into the car, he immediately stepped on the accelerator. The car roared and disappeared into the wind and snow.

When we arrived at the infirmary, there was a lot of excitement again. The female doctor in the infirmary recognized that the sick person was Ning Qingyun and did not dare to neglect at all. After a while of examination and trouble, Ning Qingyun, who had taken antipyretic medicine, finally closed her eyes and went to the infirmary.

Asleep on the hospital bed in the room.

Qin Ke held her cold little hand, put it against his face, and used his own body temperature to warm it.

Especially when he saw the girl's delicate eyebrows frowning uncomfortably, Qin Ke felt distressed again.

Although the female doctor said it was just a cold and the fever could be reduced after taking antipyretics for half an hour, Qin Ke, who had not seen Ning Qingyun sick for a long time, still stayed by the bedside.

Even when they heard some movement outside, it seemed that it was Principal Huang, Vice Principal Gu Bojun and other school leaders who were alerted and rushed over. Not long after, Academician Tian Jianlan, Academician Guo Weiyang, and Mr. Qiu also came.

Qin Ke didn't get up and leave. How could he trust Ning Qingyun, who was still suffering from a high fever, to be left alone? Not even for a short while.

Fortunately, the antipyretic medicine took effect in about half an hour. The electronic thermometer gun showed that Ning Qingyun's body temperature dropped from 39.3°C to 38.1°C, out of the category of high fever. Qin Ke also felt that the soft little hands he held slowly slowly

After the temperature returned, my hanging heart was half relieved.
To be continued...