Large-time behaviour of solutions to the outflow problem of full compressible Navier-Stokes equations

This paper is concerned with the large-time behaviour of solutions to the outflow problem of full compressible Navier-Stokes equations on the half line R+ = (0, infinity). On the basis of fine analysis, we obtain two results. One is that the non-degenerate boundary layer is stable under partially large initial perturbation. The other is that the superpositions of the boundary layer (including the non-degenerate case) and the 3-rarefaction wave are asymptotically stable under some smallness conditions. The proofs are given by the elementary energy method.