Weak and variational entropy solutions to the system describing steady flow of a compressible reactive mixture

TL;DR

This paper introduces variational entropy solutions for a model of steady compressible reactive gas flow and proves their existence under certain conditions, extending previous results with improved density estimates.

Contribution

It extends prior work by defining variational entropy solutions and establishing their existence for a broader range of the adiabatic exponent gamma.

Findings

Existence of weak solutions for gamma > 4/3

Existence of variational entropy solutions for gamma > 1

Improved density estimates underpin the proofs

Abstract

We consider a system of partial differential equations which describes steady flow of a compressible heat conducting chemically reacting gaseous mixture. We extend the result from Giovangigli, Pokorn\'y, Zatorska (2015) in the sense that we introduce the variational entropy solution for this model and prove existence of a weak solution for $\gamma >\frac 43$ and existence of a variational entropy solution for any $\gamma >1$. The proof is based on improved density estimates.