  In this paper, we prove the existence of global weak solutions for 3D
compressible Navier-Stokes equations with degenerate viscosity. The method is
based on the Bresch and Desjardins entropy conservation. The main contribution
of this paper is to derive the Mellet-Vasseur type inequality for the weak
solutions, even if it is not verified by the first level of approximation. This
provides existence of global solutions in time, for the compressible
Navier-Stokes equations, for any $\gamma>1$, in three dimensional space, with
large initial data possibly vanishing on the vacuum. This solves an open
problem proposed by Lions.
