Global Solutions of 3-D Inhomogeneous Navier-Stokes System with Large Viscosity in One Variable

Abstract

We consider the global well-posedness of three dimensional incompressible inhomogeneous Navier-Stokes equation with different viscous coefficients in the vertical and horizontal variables. In particular, when one of these viscous coefficients is large enough compared with the initial data and the initial density is close enough to a positive constant, we prove the global well-posedness of this system. This result extends the previous results in [9, 11] for the classical Navier-Stokes system.