The stability of rarefaction wave for Navier-Stokes equations in the half-line

Abstract

This paper studies the stability of the rarefaction wave for Navier–Stokes equations in the half-line without any smallness condition. When the boundary value is given for velocity u∥x = 0 = u− and the initial data have the state (v+, u+) at x + ∞, if u−<u+, it is excepted that there exists a solution of Navier–Stokes equations in the half-line, which behaves as a 2-rarefaction wave as t + ∞. Matsumura–Nishihara have proved it for barotropic viscous flow (Quart. Appl. Math. 2000; 58:69–83). Here, we generalize it to the isentropic flow with more general pressure. Copyright © 2011 John Wiley & Sons, Ltd.