Global well-posedness of the Cauchy problem for the Navier-Stokes equations of nonisentropic flow with discontinuous initial data

Abstract

We prove the global existence, uniqueness, and continuous dependence on initial data for discontinuous solutions of the Navier-Stokes equations for nonisentropic, compressible flow in one space dimension. A great deal of information is obtained concerning the qualitative behavior of the solution, including an analysis of the convection and evolution of jump discontinuities, the derivation of sharp rates of smoothing, and the L ∞ asymptotic behavior.