On steady solutions to a model of chemically reacting heat conducting compressible mixture with slip boundary conditions

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.