241214 Introduction to Boltzmann equations (S) (WiSe 2024/2025)

Description: The Boltzmann equations are nonlinear, non-local partial differential equations. They describe the evolution of the distribution of particles in a non-equilibrium dilute gas system, where the particles interact via two-particle elastic collisions. The Boltzmann equations play an important role in both mathematics and physics. Due to their complexity, many problems related to the Boltzmann equations remain open.

In this seminar, we will start with the spatially homogeneous Boltzmann equations (where the positions are degenerate) to discuss well-posedness, the H-Theorem related to dissipative entropy, and the propagation of regularities. Then, we will move on to the inhomogeneous Boltzmann equations, addressing their Cauchy problems and hydrodynamic limits to Navier-Stokes equations. The specific topics will be tailored to match the level and interests of the participants.

Prerequisites:
A course in PDE and functional analysis

Preliminary meeting:
Tuesday, July 16, 14:15 in V2-135

If you are interested in this seminar but were unable to attend the preliminary meeting, please contact: zihui.he@uni-bielefeld.de