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- Liberal arts and basic science courses
- Academic unit or major
- Graduate major in Mathematics
- Instructor(s)
- Sakamoto Shota
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- Day/Period(Room No.)
- Fri3-4(H115)
- Group
- -
- Course number
- MTH.C404
- Credits
- 1
- Academic year
- 2022
- Offered quarter
- 4Q
- Syllabus updated
- 2022/4/20
- Lecture notes updated
- -
- Language used
- English
- Access Index
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Course description and aims
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.
Student learning outcomes
Understanding of the smoothing effect of the non-cutoff Boltzmann equation
Keywords
Smoothing effect, hydrodynamical limit
Competencies that will be developed
| ✔ 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/Required learning
| Course schedule | Required learning | |
|---|---|---|
| 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. |
Out-of-Class Study Time (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.
Assessment criteria and methods
Report (100%)
Related courses
- MTH.C403 ： Advanced topics in Analysis C
Prerequisites (i.e., required knowledge, skills, courses, etc.)
Understanding of topics in Advanced topics in Analysis C is required.
