Linear Stability of Hyperbolic Moment Models for Boltzmann Equation

TL;DR

This paper investigates the linear stability of hyperbolic regularizations of Grad's moment models for the Boltzmann equation, including collision terms, demonstrating stability at local equilibrium and satisfying Yong's stability condition.

Contribution

It extends the analysis of hyperbolic moment models by incorporating collision terms and proves their linear stability with common collision models.

Findings

Models are linearly stable at local equilibrium.

Models satisfy Yong's first stability condition.

Stability holds with Boltzmann's binary collision model.

Abstract

Grad's moment models for Boltzmann equation were recently regularized to globally hyperbolic systems, and thus the regularized models attain local well-posedness for Cauchy data. The hyperbolic regularization is only related to the convection term in Boltzmann equation. We in this paper studied the regularized models with the presentation of collision terms. It is proved that the regularized models are linear stability at the local equilibrium and satisfy Yong's first stability condition with commonly used approximate collision terms, and particularly with Boltzmann's binary collision model.