  In this paper we prove the existence of global strong solution for the
Navier-Stokes equations with general degenerate viscosity coefficients. The
cornerstone of the proof is the introduction of a new effective pressure which
allows to obtain an Oleinik-type estimate for the so called effective velocity.
In our proof we make use of additional regularizing effects on the velocity
which requires to extend the technics developed by Hoff for the constant
viscosity case.
