Inviscid Limit for the Navier-Stokes Equations of Compressible, Isentropic Flow with Shock Data.

摘要

We solve the inviscid limit problem for the Navier-Stokes equations for one-dimensional, isentropic, compressible flow with shock data. We prove that the solution exists for all time, that it converges to the inviscid shock, and that it converges to the inviscid shock as the viscosity tends to zero, uniformly in space to a travelling wave for fixed viscosity, as t tends to infinity. The overall analysis provides a very detailed picture of the qualitative properties of the viscous solution. Keywords: Viscous compressible flow; Shock waves; Hyperbolic-parabolic systems. Reprints. (edc)