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

Chapter 12: A Small Step Towards Scientific Research: The Final Mission

Although there was an additional daily task, Xu Ling's life did not become much richer. There was just an inappropriate playground inserted into the straight line of teaching building - cafeteria - dormitory.

However, on Friday night of the second teaching week, after watching the system customization explanation, the taskbar that had not changed for a long time finally changed.

"Ding!"

"Mission completed! 10 motivation points have been issued, please check!"

【Ordinary tasks

(1) Library card (not collected)
……

(2) Working for the health of the motherland for 30 years
……

Glory Mission
(1) A small step towards scientific research (final task): Please complete the proof of the conjecture of global solutions of the incompressible Navier-Stokes equations with small initial values, write a paper, and publish it within ten days.

Completion reward: 30 motivation points.

Failure penalty: clear subject experience points.

Mission countdown: 9 days, 23 hours, 58 minutes.

Can it be rejected: Yes. 】

Final mission!
It turned out to be a published paper!
However, this countdown gave Xu Ling a headache. Although he had learned the system's special explanations and had his own ideas, there were still many specific details that he could not solve.

What's more, Xu Ling had no experience in writing papers. It would be fine if he could just figure it out slowly, but once a deadline was set, Xu Ling could not guarantee that his paper would fully meet expectations.

A journey of a thousand miles begins with a single step. Isn’t the path of scientific research a long and continuous climb?
With his mind made up, Xu Ling decisively accepted the task, turned on the computer and started typing.

【Proof of the existence, uniqueness, regularity and stability of global solutions for the incompressible Navier-Stokes equations with small initial values】

【Summary:
This paper focuses on the extremely challenging mathematical topic of the conjecture of small initial value global solutions for the incompressible Navier-Stokes equations.

Through systematic and in-depth analysis and the comprehensive application of various advanced mathematical theories and methods, rigorous demonstration is carried out around key dimensions such as the existence, uniqueness, regularity, stability and energy estimation of solutions.

In terms of the existence of solutions, with the help of refined function space construction and approximation methods, we explore the existence of weak solutions and smooth solutions under small initial value conditions.

...]

The abstract only roughly described the idea of ​​the proof, but Xu Ling still deleted, revised, and wrote it stumblingly until one o'clock in the morning.

The specific proof has not yet been written.

Never mind! Go to sleep first!
Xu Ling turned off the computer and climbed straight onto the bed.

……

"Auntie! Give me two buns!"

At eight o'clock in the morning, Xu Ling packed up his things and went to the cafeteria.

The cafeteria was a bit deserted on weekends, with the entire hall empty and few people around.

"Student, since you came so early, I will pick two big ones for you." The cafeteria aunt said with a smile.

"Thank you, aunt!"

Xu Ling's little mouth looked as if it was covered with honey. The cafeteria aunt giggled and gave Xu Ling a cup of soy milk.

Carrying the hot buns, Xu Ling ate as he walked and soon arrived at the library.

After finishing breakfast at the door, Xu Ling walked into the library.

As usual, I found a seat by the window, turned on the computer, and also took the opportunity to complete the library check-in task.

Just as he sat down, Xu Ling heard a familiar voice:
"Xu Ling? You're here too! That's great! I can come to you if I need help!"

It’s Lin Yuxin.

But Lin Yuxin is a little different today...

She was wearing a black short jacket and a grey short skirt below her waist.

What's on those legs? Stockings? Or the legendary bare-leg artifact?

Lin Yuxin's face was also quite striking. With her light makeup, a touch of blush, and a lip gloss that was flattering but not overly coquettish, she instantly shone brightly.

Xu Ling's eyes were wide open.

Looking at Xu Ling's reaction, Lin Yuxin's face turned slightly red, but she was more proud.

You forgot about me before, but you will remember me this time, right?

"Hmm... aren't you cold?" Xu Ling asked inexplicably. "What do you care?" Lin Yuxin's expression instantly turned cold.

This guy! Will he die if I praise him?

Xu Ling was puzzled, thinking that he cared about her, so why did she have such an expression.

I really don’t understand!

Xu Ling shook his head and focused his attention on his computer.

Seeing that Xu Ling ignored her, Lin Yuxin gritted her teeth, took the book, and sat opposite Xu Ling.

"Hey! Let me see this question." Lin Yuxin took out a draft paper and handed it to Xu Ling.

Is this how you ask for help?

Xu Ling grumbled in his heart, but still took the draft paper from Lin Yuxin.

It turned out to be a question about electromagnetism!
A conducting sphere with radius R is centered at point o on the x-axis and placed in a uniform external field E0 parallel to the x-axis in electrostatic equilibrium. Find:

a. Charge density on the conductor surface
b. The electric potential energy of the conducting ball in the external field E0

The electric field strength at a distance r from the center of the sphere on the cx axis

This problem is indeed difficult to solve directly using Gauss's theorem, loop theorem, etc. However, it is easy to solve if we use an equivalent idea.

"A conducting sphere in electrostatic equilibrium can be equivalent to an electric dipole at its center..."

Xu Ling roughly explained the idea behind this question.

Although Lin Yuxin was somewhat dissatisfied with Xu Ling's emotional intelligence, she had nothing to say about his IQ.

With an idea in mind, Lin Yuxin solved the problem quickly and finished it in a few minutes.

Xu Ling couldn't help but sigh.

Is she just pretending to sleep in class? I haven't been to the library in a long time, so does she come here every day?
Xu Ling suddenly felt a chill on his back.

The sense of urgency was instantly aroused, and Xu Ling did not dare to slack off anymore. He immediately immersed himself in his mathematical proof.

……

At noon, Lin Yuxin packed up her things and was about to leave when she saw Xu Ling still staring intently at his computer. She was curious and walked behind him.

Is this what he's been researching?

Why can't I understand anything at all?
Who is the junior?
Lin Yuxin felt a little complicated: As expected, your university and my university seem to be different.

Without disturbing Xu Ling, Lin Yuxin left the library silently.

……

Um?What about people?

Looking at the empty seats, Xu Ling was a little confused.

Depend on!
It's two o'clock in the afternoon!
Seeing the time, Xu Ling was startled.

I haven’t eaten yet!

Thinking of this, Xu Ling hurriedly got up and packed his things.

"Xu Ling, you haven't eaten yet, right? I brought you some food, let's go eat outside!"

Just as I was about to turn off the computer, a voice like the sound of nature rang out.

Turning around, Lin Yuxin was holding a lunch box and looking at him quietly.

Hey? This question was not taught in vain, people remember it!
Xu Ling happily took the bag from Lin Yuxin's hand and went outside the library to eat.

One meat dish, one vegetable dish, and one soup.

really not bad!
After dinner, the two of them remained in the same position as in the morning and continued to look at their own things. During this time, Lin Yuxin asked Xu Ling several questions about electromagnetism, and Xu Ling patiently answered them.

Who made him eat other people's food?
But when it was dinner time, Lin Yuxin told Xu Ling that she would not bring him any food and that she would not come in the evening.

Xu Ling was a little disappointed, so he simply followed Lin Yuxin out of the library.

……

(End of this chapter)