Heat-Conducting, Compressible Mixtures with Multicomponent Diffusion: Construction of a Weak Solution

We investigate a coupling between the compressible Navier–Stokes–Fourier system and the full Maxwell-Stefan equations. This model describes the motion of chemically reacting heat-conducting gaseous mixture. The viscosity coefficients are density-dependent functions vanishing on vacuum and the internal pressure depends on species concentrations. By several levels of approximation we prove the global-in-time existence of weak solutions on the three-dimensional torus.