In this paper, the authors study the free boundary problem for one-dimensional compressible Navier-Stokes equations when the viscosity coefficient μ(ρ)=1+θρθ. The initial density is assumed to be connected to vacuum discontinuously. Firstly, the positive upper and lower bound of the density ρ is obtained by using some a priori estimates, and then the smooth approximate solutions are constructed by defining the approximate initial data. Finally, the authors prove the existence and uniqueness of global weak solutions when θ>0 and the interface behavior, the asymptotic behavior of solutions are also obtained. Moreover, the regularity of global solution is stablished under appropriate assumptions imposed on the initial data, and then the existence of global strong solutions is proved.
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