Stability of rarefaction wave for compressible Navier-Stokes equations on the half line

Abstract

This paper is concerned with the large-time behavior of solutions to an initial-boundary-value problem for full compressible Navier-Stokes equations on the half line (0,∞), which is named impermeable wall problem. It is shown that the 3-rarefaction wave is stable under partially large initial perturbation if the adiabatic exponent γ is close to 1. Here partially large initial perturbation means that the perturbation of absolute temperature is small, while the perturbations of specific volume and velocity can be large. The proof is given by the elementary energy method.