Continuous dependence in L2 for discontinuous solutions of the viscous p-system

Abstract

We prove that discontinuous solutions of the Navier-Stokes equations for isentropic or isothermal flow depend continuously on their initial data in L2. This improves earlier results in which continuous dependence was known only in a much stronger norm, a norm inappropriately strong for the physical model. We also apply our continuous dependence theory to obtain improved rates of convergence for certain finite difference approximations.