Remark on compressible Navier-Stokes equations with density-dependent viscosity and discontinuous initial data

In this paper, we study the free boundary problem for 1 D compressible Navier-Stokes equations with density-dependent viscosity. We focus on the case where the viscosity coefficient vanishes on vacuum. We prove the global existence and uniqueness for discontinuous solutions to the Navier-Stokes equations when the initial density is a bounded variation function, and give a decay result for the density as t -> +infinity. (c) 2007 Elsevier Inc. All rights reserved.