Optimal Decay Rate to the Contact Discontinuity for the 1D Compressible Navier–Stokes Equations With a Reacting Mixture

ABSTRACT In this paper, we investigate the large‐time asymptotic behavior of contact waves in the 1D compressible Navier–Stokes equations with a reacting mixture. We derive the optimal decay rate for generic initial perturbations, meaning that the zero‐mass condition is not required. In this paper, we refine the estimates for both anti‐derivatives and the original perturbations. We then introduce an innovative transformation to ensure that the structural conditions continue to hold for the system of derivatives. With this approach, we achieve better estimates for the derivatives, leading to the optimal decay rates. The method can be applied to a wider and more general system.