Asymptotic behavior of global weak solutions to 1D compressible Navier-Stokes equations

One-dimensional compressible Navier-Stokes equations with free boundary value problem is studied.The initial density is assumed to be connected to vacuum discontinuously.The positive upper and lower bound of the density ρ is obtained by using some priori estimates,and then smooth approximate solutions are constructed by defining the approximate initial data.The existence of global weak solutions is proved when the viscosity coefficient μ(ρ)=1+θρθ,θ0.Moreover,asymptotic behavior of global weak solutions is discussed.