A multifluid model with chemically reacting components -- construction of weak solutions

TL;DR

This paper proves the existence of global weak solutions for a complex multi-component chemically reacting fluid system, accommodating vacuum states and multiple components with both diffusing and non-diffusing elements.

Contribution

It introduces a novel mathematical framework that handles arbitrary numbers of components, nonlinear pressure-density relations, and the presence of vacuum in chemically reacting fluid models.

Findings

Existence of global weak solutions with bounded densities.

Strong compactness of densities in $L^p$ spaces under positivity assumptions.

Framework applicable to high-general models with diffusing and non-diffusing elements.

Abstract

We investigate the existence of weak solutions to a multi-component system, consisting of compressible chemically reacting components, coupled with the compressible Stokes equation for the velocity. Specifically, we consider the case of irreversible chemical reactions and assume a nonlinear relation between the pressure and the particular densities. These assumptions cause the additional difficulties in the mathematical analysis, due to the possible presence of vacuum. It is shown that there exists a global weak solution, satisfying the $L^\infty$ bounds for all the components. We obtain strong compactness of the sequence of densities in $L^p$ spaces, under the assumption that all components are strictly positive. The applied method captures the properties of models of high generality, which admit an arbitrary number of components. Furthermore, the framework that we develop can handle models that contain both diffusing and non-diffusing elements.