Nonlinear stability of rarefaction waves for one-dimensional compressible Navier–Stokes equations for a reacting mixture

Abstract

In this paper, we study the long-time behavior toward rarefaction waves for the Cauchy problem to a one-dimensional Navier–Stokes equations for a reacting mixture. It is shown that under the condition adiabatic exponent $$\gamma $$ is close to 1, the global stability is established. In this paper, the initial perturbation can be large.