Asymptotic Stability of Global Solutions to Non-isentropic Navier–Stokes Equations

Abstract

This paper studies the asymptotic stability of global solutions of the three-dimensional nonisentropic compressible Navier–Stokes equations, where the initial data satisfy the “well-prepared” initial conditions, and the velocity field and temperature satisfy the Dirichlet boundary condition and convective boundary condition, respectively, based on the incompressible limit of global solutions. With the uniform estimates with respect to both the Mach number $\epsilon$ and time $t$ , we prove the exponentially asymptotic stability for global solutions of both the compressible Navier–Stokes equations and its limiting incompressible equations.