2022 Faculty Courses School of Science Department of Mathematics Graduate major in Mathematics
Advanced topics in Analysis D
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Shota Sakamoto
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 3-4 Fri (H115)
- Class
- -
- Course Code
- MTH.C404
- Number of credits
- 100
- Course offered
- 2022
- Offered quarter
- 4Q
- Syllabus updated
- Jul 10, 2025
- Language
- English
Syllabus
Course overview and goals
The main subject of this course is the non-cutoff Boltzmann equation. In particular, the smoothing effect of the equation will be discussed in detail. Hydrodynamical limits will be explained if time permits.
This course is following Advanced topics in Analysis C.
Course description and aims
Understanding of the smoothing effect of the non-cutoff Boltzmann equation
Keywords
Smoothing effect, hydrodynamical limit
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
This is a standard lecture course. Occasionally some problems for reports are given.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Different aspects of the non-cutoff and cutoff Boltzmann equations | Details will be provided during each class session. |
| Class 2 | Cancellation lemma and a coercivity estimate | Details will be provided during each class session. |
| Class 3 | Smoothing effect 1: The main result of AMUXY (2011, ARMA) | Details will be provided during each class session. |
| Class 4 | Smoothing effect 2: Upper estimates of the collision operator | Details will be provided during each class session. |
| Class 5 | Smoothing effect 3: Lower estimates of the collision operator | Details will be provided during each class session. |
| Class 6 | Hydrodynamical limit 1: The Hilbert expansion | Details will be provided during each class session. |
| Class 7 | Hydrodynamical limit 2: Knudsen number, Mach number and various fluid equations | Details will be provided during each class session. |
Study advice (preparation and review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
Not required
Reference books, course materials, etc.
Given during the lectures.
Evaluation methods and criteria
Report (100%)
Related courses
- MTH.C403 ： Advanced topics in Analysis C
Prerequisites
Understanding of topics in Advanced topics in Analysis C is required.