Global Weak Solutions to One-Dimensional Compressible Navier-Stokes Equations with Density-Dependent Viscosity

Abstract. We prove the global existence of weak solutions of the one-dimensional compressible Navier-stokes equations with density-dependent viscosity. In particu-lar, we assume that the initial density belongs to L1 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. AMS Subject Classifications: 35D0