Stationary solutions for the ellipsoidal BGK model in a slab

TL;DR

This paper proves the existence and uniqueness of stationary solutions for the ellipsoidal BGK model of the Boltzmann equation in a bounded slab, under specific boundary and rarefaction conditions.

Contribution

It establishes the first rigorous existence and uniqueness results for stationary solutions of the ellipsoidal BGK model in a bounded domain.

Findings

Unique mild solutions exist under boundary data constraints.

Solutions are valid for sufficiently rarefied gases.

Boundary data must not concentrate excessively around zero velocity.

Abstract

We address the boundary value problem for the ellipsoidal BGK model of the Boltzmann equation posed in a bounded interval. The existence of a unique mild solution is established under the assumption that the inflow boundary data does not concentrate too much around the zero velocity, and the gas is sufficiently rarefied.