LARGE-TIME BEHAVIOR OF COMPOSITE WAVES OF VISCOUS SHOCKS FOR THE BAROTROPIC NAVIER-STOKES EQUATIONS

Abstract

We study the large-time behavior of the one-dimensional barotropic Navier-Stokes flow perturbed from Riemann data generating a composition of two shock waves with small amplitudes. We prove that the perturbed Navier-Stokes flow converges, uniformly in space, toward a composition of two viscous shock waves as time goes to infinity, up to dynamical shifts. Especially, the strengths of the two waves can be chosen independently. This is the first result for the convergence to a composite wave of two viscous shocks with independently small amplitudes.