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

TL;DR

This paper establishes the existence of stationary solutions for a broad class of discrete velocity Boltzmann equations in two dimensions, using approximation sequences and compactness arguments.

Contribution

It provides a rigorous proof of stationary solutions for discrete velocity Boltzmann equations with boundary conditions in the plane, expanding theoretical understanding.

Findings

Existence of renormalized stationary solutions proven.

Construction of approximation sequences with L1 compactness.

Application of Kolmogorov-Riesz theorem for compactness.

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 L1 compactness for the integrated collision frequency and gain term. Compactness is obtained using the Kolmogorov-Riesz theorem.