Stationary Solutions to the Two-Dimensional Broadwell Model

Abstract

Existence of renormalized solutions to the two-dimensional stationary Broadwell model in a square with given indata in $L^1$ is proven. Averaging techniques from the continuous velocity case being unavailable when the velocities are discrete, the approach is based on direct $L^1$-compactness arguments using the Kolmogorov-Riesz theorem.