Decay rate to contact discontinuities for the one-dimensional compressible Navier–Stokes equations with a reacting mixture

Abstract

In this paper, we investigate the nonlinear stability of contact waves for the Cauchy problem to the compressible Navier–Stokes equations for a reacting mixture in one dimension. If the corresponding Riemann problem for the compressible Euler system admits a contact discontinuity solution, it is shown that the contact wave is nonlinearly stable, while the strength of the contact discontinuity and the initial perturbation are suitably small. Especially, we obtain the convergence rate by using anti-derivative methods and elaborated energy estimates.