Asymptotic stability of nonlinear wave for the compressible Navier-Stokes equations in the half space (Q927651)

The authors consider the initial-boundary value problem for the one-dimensional isentropic compressible Navier-Stokes equations in the half space. The problem is the outflow problem, i.e.\ the velocity on the bound is negative. The focus is at the large-time behaviour of the solution. The space-symptotic states and the boundary data are assumed to satisfy sertain condition so that the solution is a nonlinear wave which is the superposition of a stationary solution and a rarefaction wave. It is proved that this wave is nonlinearly stable under small perturbations.