  In this paper, we study the vanishing viscosity limit of one-dimensional
isentropic compressible Navier-Stokes equations with density-dependent
viscosity, to the isentropic compressible Euler equations. Based on several new
uniform estimates to the viscous systems, in addition to the framework recently
established by G. Chen and M. Perepelitsa, we justify that the finite energy
solution of the isentropic compressible Euler equations for a large class of
initial data can be obtained as the inviscid limit of the compressible
Navier-Stokes equations even when the viscosity depends on the density.
