Asymptotic stability of rarefaction wave of the Cauchy problem for viscous conservation laws

This paper is concerned with the asymptotic stability of rarefaction waves for the two-dimensional steady isentropic irrotational flow with artificial viscosity. We prove that if the initial value is close to a constant state and the corresponding inviscid hyperbolic system admits a weak rarefaction wave, then the solution tends to this rarefaction wave as t→∞.