Mixtures: sequential stability of variational entropy solutions

TL;DR

This paper proves the sequential stability of variational entropy solutions for a complex model of reactive gas mixtures, considering variable viscosity and thermodynamic constraints.

Contribution

It introduces a stability analysis for weak variational entropy solutions in multi-component reactive gas mixtures with specific thermodynamic and diffusion properties.

Findings

Proved stability of entropy solutions under specified conditions.

Established mathematical framework for reactive gas mixture models.

Addressed challenges posed by vanishing viscosity coefficients.

Abstract

The purpose of this work is to analyze the mathematical model governing motion of $n$-component, heat conducting reactive mixture of compressible gases. We prove sequential stability of weak variational entropy solutions when the state equation essentially depends on the species concentration and the species diffusion fluxes depend on gradients of partial pressures. Of crucial importance for our analysis is the fact that viscosity coefficients vanish on vacuum and the source terms enjoy the admissibility condition dictated by the second law of thermodynamics.