Global stability of viscous contact wave for compressible Navier–Stokes equations with temperature‐dependent transport coefficients and large data

Abstract

We are concerned with the large‐time behavior of the viscous contact wave for a one‐dimensional compressible Navier–Stokes equations whose transport coefficients depend on the temperature. It is shown that if the adiabatic exponent satisfies a suitable inequality and strength is small enough, the unique solution global in time to ideal polytropic gas exists and asymptotically tends toward the viscous contact wave under large initial perturbation for any . Subsequently, we also prove that the large‐time asymptotic stability of the contact wave has a uniform convergence rate under initial data. Our results improve ‐rate in [F. Huang, Z. Xin, and T. Yang, Adv. Math. 219 (2008), 1246–1297] which studied the constant coefficients Navier–Stokes system. The proofs are given by the elementary energy estimate and anti‐derivative method.