Hypocoercivity for a BGK model for gas mixtures

TL;DR

This paper establishes exponential convergence to equilibrium for a linearized BGK model of a two-component gas mixture by constructing an entropy functional and adapting spectral methods, extending previous single-species results.

Contribution

It extends hypocoercivity analysis to a coupled two-species BGK model, incorporating interspecies interactions into the entropy framework.

Findings

Proves exponential relaxation to equilibrium with explicit rates.

Develops an entropy functional for the coupled system.

Adapts spectral and Lyapunov methods to the two-species case.

Abstract

We consider a kinetic model for a two component gas mixture without chemical reactions. Our goal is to study hypocoercivity for the linearized BGK model for gas mixtures in continuous phase space. By constructing an entropy functional, we can prove exponential relaxation to equilibrium with explicit rates. Our strategy is based on the entropy and spectral methods adapting Lyapunov's direct method as presented in [Achleitner-Arnold-Carlen, 2016] for the one species linearized BGK model. In comparison to the one species case, we start with two partial differential equations, one for each species. These equations are coupled due to interspecies interactions, which requires additional estimates on these interspecies terms.