Asymptotic behavior of solutions to the full compressible Navier-Stokes equations in the half space

Abstract

The one-dimensional motion of compressible viscous and heat-conductive fluid is investigated in the half space. By examining the sign of fluid velocity prescribed on the boundary, initial boundary value problems with Dirichlet type boundary conditions are classified into three cases: impermeable wall problem, inflow problem and outflow problem. In this paper, the asymptotic stability of the rarefaction wave, boundary layer solution, and their combination is established for both the impermeable wall problem and the inflow problem under some smallness conditions. The proof is given by an elementary energy method.