Global existence for fully nonlinear reaction–diffusion systems describing multicomponent reactive flows

Abstract

We consider combustion problems in the presence of complex chemistry and nonlinear diffusion laws leading to fully nonlinear multi-species reaction–diffusion equations. The nonlinear diffusion coefficients are obtained by resolution of the so-called Stefan–Maxwell equations that we discuss thoroughly. The reaction diffusion equations are coupled with the Navier–Stokes equations and the heat equation in the context of a typical combustion problem. We establish results of existence of solutions in space dimensions two and three.