Global existence of large strong solutions to the 3D barotropic compressible Navier-Stokes equations with density-dependent viscosities

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, defining suitable energy functionals, and using a totally different iteration scheme, 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.