Discrete velocity Boltzmann eqations in the plane:stationary solutions for a generic class

Abstract

The paper proves existence of renormalized stationary solutions for a dense class of discrete velocity Boltzmann equations in the plane with given ingoing boundary values. The proof is based on the construction of a sequence of approximations with L 1 compactness for the integrated collision frequency and gain term. Compactness is obtained using the Kolmogorov-Riesz theorem, which replaces the L 1 compactness of velocity averages in the continuous velocity case, not available when the velocities are discrete. .