Viscosity Coefficient Dependent On The Density Of One-dimensional Pressure To The Existence Of Global Weak Solutions To The Navier-stokes Equations

In this paper,we prove the global existence of weak solutions of the Navier-Stokes equations of compressible flows in one space dimensional with densitydependent viscosity.In particular,we require that the initial density belongs to L~1(R)and L~∞(R),and may take different constont at x =-∞and x = +∞.The initial vacuum is permitted in this paper and the results may apply to the one dimensional Saint-Venant for shallow water.