I failed a course, and the system became my study supervisor.

Chapter 8 Incompressible Navier-Stokes Equations
In general, Xu Ling decided to explore the proof of the conjecture of global solution with small initial values.

Because when studying the supplementary materials, Xu Ling already had his own understanding of this aspect, especially the partial differential equations involving time and space variables or special equations with one-dimensional symmetry.

As for what is the global solution with small initial values?
In fact, it is very easy to understand. When the given initial value is small enough in a certain range, the equation has a unique global smooth solution.

Although he had figured out the general direction, Xu Ling was still a little hesitant about which mathematical physics equation to choose as the focus of his research.

No investigation, no right to speak!
Early the next morning, Xu Ling came to the library and collected a lot of information from all aspects. He also took the opportunity to take on the library check-in task.

It's not just for the 10 diligence points, but more about taking advantage of the auxiliary functions of the task.

After running around, a small mountain of books piled up in front of Xu Ling. From some angles, Xu Ling could not be seen.

Gauge Field Theory, Foundations of General Relativity, Gravitation and Spacetime, Modern Numerical Methods for Mathematical Physics Equations, Adaptability Theory of Incompressible Navier-Stokes Equations, Nonlinear Evolution Equations...

These books, which Xu Ling would normally not even glance at, were now being read eagerly by him.

After continuous absorption and learning, Xu Ling gradually determined his choice.

Incompressible Navier-Stokes equations!

The most important reason is that this equation describes the motion law of viscous incompressible fluid and is the content of fluid mechanics.

Fluid mechanics was discussed in detail in Xu Ling's theoretical mechanics course, so Xu Ling is relatively familiar with it.

If you hesitate to make a decision, you will suffer from the chaos. In order to avoid getting stuck in the dilemma, Xu Ling decisively accepted the task and confirmed his research focus.

"Ding!"

"The research focus has been determined. Please receive the customized information on time. No latecomers will be accepted!"

Hearing the system prompt, Xu Ling breathed a sigh of relief.

The first step has been taken, hasn't it?

At this moment, a familiar voice came to Xu Ling's ears:

"Eh? Xu Ling, you're here too!"

Following the voice, Xu Ling turned his head and saw Wang Xueqin holding a book and looking at him with a smile.

"Teacher Wang?" Xu Ling was a little surprised. "Hello, hello."

"Are there any problems with your make-up exam?" Wang Xueqin asked softly.

"No problem!" Xu Ling said confidently.

"That's fine. Eh? Why are you reading these books? They're pretty difficult!"

"Nothing, just looking around." Xu Ling scratched his head.

Wang Xueqin changed the subject and said, "Oh right! Course selection starts tomorrow. You should take an electromagnetics course. I suggest you take Professor Zhang Zhongyao's class. He's a very good lecturer and he's also my advisor."

"Okay, I'll remember it!" Xu Ling nodded repeatedly.

The two exchanged a few more pleasantries, and then Wang Xueqin left with the book.

Xu Ling read the book very clearly, it was "Description of Magnetohydrodynamic Motion".

Without paying too much attention, Xu Ling considered Wang Xueqin's suggestion.

Professor Zhang Zhongyao?

As soon as the thought came to his mind, Xu Ling took out his mobile phone and asked Baidu.

Zhang Zhongyao, a native of Jinling, Jiangsu Province, is currently the Vice Dean of the School of Physics at Shanghai University. He specializes in electromagnetics and is a world-renowned scholar in this field, having won the first prize of the National Natural Science Award.

Damn! This is awesome!
No wonder some people always jokingly call university teachers the most impressive people they have ever met.

After reading Professor Zhang’s introduction, Xu Ling was shocked, but also became determined: he must choose Professor Zhang’s class!
But class selection was for the next day. Tonight, Xu Ling was extremely excited for something else: the customized explanation from the system. ...

Ten o'clock in the evening arrived as scheduled, and Xu Ling was waiting in front of the computer early.

Seeing a video file appear out of thin air on his computer desktop again, Xu Ling couldn't help but marvel at it.

Put on the headphones, click play, and then a serious voice comes out:
"...

What is the difficulty in proving the global solution of the three-dimensional incompressible Navier-Stokes equations with small initial values?
The reason is that in the three-dimensional state, the equation has a highly nonlinear structure, coupled with the complexity of fluid motion, such as the existence of eddies, turbulence and other motions.

......"

So that's how it is! Xu Ling suddenly realized that the complexity of the motion made it even more difficult to prove the uniqueness of the solution.

So what are the feasible methods at present?

The video also gives an introduction:

"Energy estimation methods are commonly used. By estimating physical quantities such as the fluid's kinetic energy and vorticity, energy inequalities are constructed to control the growth of the solution."

"In addition, Fourier analysis is also an important method. Using Fourier transform, we can better characterize the various properties of functions."

Xu Ling was not familiar with the energy estimation method, but he was familiar with Fourier analysis!

The study of this equation began with the application of Fourier analysis.

However, before Xu Ling could hear the detailed explanation of Fourier analysis, the entire video had already ended.

Xu Ling was startled and quickly checked the taskbar. Fortunately, the task was not over yet, which meant the explanation would continue.

After shutting down his computer, Xu Ling stopped studying. The intense study throughout the day had already exhausted him, and his temples were already aching slightly.

Why not see which courses I need to choose tomorrow? Xu Ling thought as he logged into the academic affairs system.

School of Physics - Freshman Spring Semester Training Program:

Linear algebra

Abstract Algebra
电磁学

Thermodynamics and Statistical Physics (Part 2)
Basic Physics Experiments
By investigating the course review community, Xu Ling also found high-scoring teachers for subjects other than electromagnetism.

However, when Xu Ling read previous students' evaluations of basic university physics experiments, he was shocked.

All bad reviews!

Many students posted indignant comments, denouncing the course as pure torture.

So scary? Xu Ling was a little scared and quickly read through the posts. In the end, he found three major flaws in the experimental class:
The experiment was difficult to conduct, the experimental report was difficult to write, and the final score was not good.

As a poor student with a lot of problems, Xu Ling felt relieved after seeing this. He just wanted to say one thing to those students:
If you're not good at it, practice more! Don't blame the course for being too difficult!
The rules for course selection are also clearly written in the announcement of the academic affairs system:

2月25日上午8:00到12:00，全体学生进行第一轮选课。

The draw will be held from 14:00 PM to 16:00 PM.

18:00 Students complete course selection based on the lottery results.

Xu Ling didn't pay much attention to this process last semester. He didn't care which teacher's class he chose before, as long as he had the class.

But now, Xu Ling is very nervous. The lottery has always been very abstract in the eyes of students, and there are many cases where students failed to get any courses in the first round of course selection.

What if he wasn't chosen? Xu Ling didn't dare to think about it anymore.

(End of this chapter)