CONTINUOUS DEPENDENCE ON INITIAL DATA FOR DISCONTINUOUS SOLUTIONS OF THE NAVIER-STOKES EQUATIONS FOR ONE-DIMENSIONAL, COMPRESSIBLE FLOW

We prove that discontinuous solutions of the Navier-Stokes equations f or one-dimensional, compressible fluid flow depend continuously on the ir initial data. Perturbations in the different components are measure d in various fractional Sobolev norms; L(2) bounds are then obtained b y interpolation. This improves upon earlier results in which continuou s dependence was known only in a much stronger topology, one inappropr iately strong for the physical model. More generally, we derive a boun d for the difference between exact and approximate weak solutions in t erms of their initial differences and of the weak truncation error ass ociated with the approximate solution.