Viscous Coefficient Of Density-dependent Compressible Navier-stokes Equations,

The Navier-Stokes systems for one-dimensional compressible fluids with densitydependent viscosities when the initial density connects to vacuum continuously are considered in the prensent paper.Precisely,when the viscosity coefficientμis proportional toρ~θand 1/2＜θ＜3/2,whereρis the density,the global existence of weak solutions is proved.Moreover,no matter how the global weak solutions of the system for anyθ＞0 exists or not,we obtain a stabilization rate estimates of the density as t�'∞.That means that the density tends to zero as time tends to infinite.In particular,it fits for the one-dimensional Saint-Venant modal for shallow water.