1. Introduction

This course is to introduce the mathematical theory on the solutions of the Boltzmann equations

and to consider the decay analysis.

 

2. Outline & Descriptions

In the lectures, we first revisit Caflisch’s decomposition of the Boltzmann equation and combine it with spectral analysis

and energy estimates to construct global Boltzmann solutions close to equilibrium, featuring slow velocity decay in the

case of the whole space. Both cutoff and non-cutoff scenarios will be considered within different functional frameworks.

Second, we examine non-equilibrium solutions to the Boltzmann equation with shearing effects, where slower polynomial

velocity decay becomes a crucial characteristic of the solutions. The long-term dynamics under shearing depend on the

type of intermolecular interaction potentials, and we analyze both Maxwell molecules and hard potentials. Third, we explore

the initial-boundary value problem for the Boltzmann equation in the context of Couette flow, considering both finite and

vanishing Knudsen numbers. Finally, we discuss several problems related to these topics.

 

3. Registration

https://forms.gle/9UuBzkZqich9jyHw8

 

4. Join Online

May 11    May 12