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 courses in Analysis C.
Understanding of the smoothing effect of the non-cutoff Boltzmann equation
Smoothing effect, hydrodynamical limit
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
This is a standard lecture course. Occasionally some problems for reports are given.
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. |
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.
None
Given during the lectures.
Report (100%)
Understanding of topics in Advanced courses in Analysis C is required.
sakamoto.s.aj[at]m.titech.ac.jp