Shock waves for compressible navier‐stokes equations are stable

It is shown that shock waves for the compressible Navier‐Stokes equations are nonlinearly stable. A perturbation of a shock wave tends to the shock wave, properly translated in phase, as time tends to infinity. Through the consideration of conservation of mass, momentum and energy we obtain an a priori estimate of the amount of translation of the shock wave and the strength of the linear and nonlinear diffusion waves that arise due to the perturbation. Our techniques include the energy method for parabolic‐hyperbolic systems, the decomposition of waves, and the energy‐characteristic method for viscous conservation laws introduced earlier by the author.