On the stationary flow of a reactive gaseous mixture

We are interested in a system of equations describing stationary flow of a mixture of gases undergoing reversible chemical reactions. The system consists of the stationary compressible Navier-Stokes-Fourier equations coupled with reaction-diffusion equations describing balance of fractional masses.In particular we admit strong cross-diffusion, however we assume that molar masses of all species are equal.
After presenting the model and brief overview of known results I will show the entropy inequality which is the source of crucial estimates used in the proof of existence of solutions. Then I will sketch the proof of existence of weak solutions and so called variational entropy solutions.
The talk will be based on joint results with Milan Pokorny.