Compressible Navier-Stokes equations with vacuum state in the case of general pressure law

In this paper, we consider the one-dimensional compressible isentropic Navier-Stokes equations with a general 'pressure law' and the density-dependent viscosity coefficient when the density connects to vacuum continuously. Precisely, the viscosity coefficient mu is proportional to rho(theta) and 0 < theta < 1, where rho is the density. And the pressure P=P(rho) is a general 'pressure law'. The global existence and the uniqueness of weak solutions is proved, and a decay result for the pressure as t --> + infinity is given. It is also proved that no vacuum states and no concentration states develop, and the free boundary do not expand to infinite. Copyright (C) 2006 John Wiley & Sons, Ltd.