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. 
Piotr Bogs{\l}aw Mucha and Milan Pokorn\'y and Ewelina Zatorska
math.AP