On stationary solutions to normal, coplanar, discrete Boltzmann equation models

TL;DR

This paper establishes the existence of stationary solutions for a class of discrete Boltzmann equations in a coplanar setting, using advanced compactness techniques to handle the collision terms.

Contribution

It provides a rigorous proof of existence for renormalized solutions to velocity-discrete coplanar stationary Boltzmann equations, employing Kolmogorov Riesz compactness methods.

Findings

Existence of renormalized solutions proven.

Construction of approximation sequences with L1 compactness.

Application of Kolmogorov Riesz theorem for compactness.

Abstract

The paper proves existence of renormalized solutions for a class of velocity-discrete coplanar stationary Boltzmann equations with given indata. The proof is based on the construction of a sequence of approximations with L1 compactness for an integrated collision frequency and gain term. The compactness is obtained using the Kolmogorov Riesz theorem.