Local C1 solutions to some non-linear PDE system

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 P(theta)and 0<(theta)<1, where P is the density. And the pressure P = P(P) 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(right arrow) + (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.