Global Weak Solutions to One-dimensional Compressible Navier-Stokes Equations with Density-dependent Viscosity Coefficients

Abstract

We prove the global existence of weak solutions of the one-dimensional compressible Navier-stokes equations with density-dependent viscosity. In particular, we assume that the initial density belongs to L^1 and L^∞, module constant states at x=-∞ and x=+∞, which may be different. The initial vacuum is permitted in this paper and the results may apply to the one-dimensional Saint-Venant model for shallow water.