Nonlinear stability of rarefaction waves for compressible Navier Stokes equations

Abstract

It is shown that expansion waves for the compressible Navier-Stokes equations are nonlinearly stable. The expansion waves are constructed for the compressible Euler equations based on the inviscid Burgers equation. Our result shows that Navier-Stokes equations and Euler equations are time-asymptotically equivalent on the level of expansion waves. The result is proved using the energy method, making essential use of the expansion of the underlining nonlinear waves and the specific form of the constitutive eqution for a polytropic gas.