  In this paper, we consider the Cauchy problem for the three-dimensional
barotropic compressible Navier-Stokes equations with density-dependent
viscosities. By considering the system as an elliptic-dominated structure and
defining suitable energy functionals, after the elaborate index analysis, we
establish the global existence of strong solutions as long as the initial data
is large enough. This is a big contrast to the classical results where the
initial data is a small perturbation of some resting states.
