Asymptotic Behavior of the Solution to Compressible Navier–Stokes System with Temperature-Dependent Heat Conductivity in an Unbounded Domain

Abstract

This paper concerns the one-dimensional compressible Navier–Stokes system with temperature-dependent heat conductivity in R with large initial data. We prove that velocity and temperature are uniformly bounded from below and above in time and space when the heat conductivity coefficient takes κ=κ¯(1+θb) for all b>52. In addition, we show that the global solution is asymptotically stable as time tends to infinity.