Stability of Contact Discontinuity with General Perturbation for the Compressible Navier-Stokes Equations with Reaction Diffusion

Abstract

In this article,for the compressible Navier-Stokes equations which have reaction diffusion, the stability of contact discontinuities is considered. The new characteristic for the flow is appearance of the divergence between energy gained and lost because of the reaction . In the energy equations,the term related to the mass fraction of the reactant leads to new technical problem. To solve this problem, in terms of the solutions,a new system should be set up. Using the anti-derivative method and the elaborated energy method, we obtain that as long as the general perturbation of the initial datum plane and the strength of the contact wave are properly small, the contact wave is nonlinear and stable. As a byproduct, we can establish the convergence velocity of contact wave.