On the motion of a viscous compressible radiative-reacting gas

A multidimensional model is introduced for the dynamic combustion of compressible, radiative and reactive gases. In the macroscopic description adopted here, the radiation is treated as a continuous field, taking into account both the wave (classical) and photonic (quantum) aspects associated with the gas [20, 36]. The model is formulated by the Navier-Stokes equations in Euler coordinates, which is now expressed by the conservation of mass, the balance of momentum and energy and the two species chemical kinetics equation. In this context, we are dealing with a one way irreversible chemical reaction governed by a very general Arrhenius-type kinetics law. The analysis in the present article extends the earlier work of the authors [17], since it now covers the general situation where, both the heat conductivity and the viscosity depend on the temperature, the pressure now depends not only on the density and temperature but also on the mass fraction of the reactant, while the two species chemical kinetics equation is of higher order. The existence of globally defined weak solutions of the Navier-Stokes equations for compressible reacting fluids is established by using weak convergence methods, compactness and interpolation arguments in the spirit of Feireisl [26] and P.L. Lions [35].