  The purpose of this paper is to provide a large class of initial data which
generates global smooth solution of the 3-D inhomogeneous incompressible
Navier-Stokes system in the whole space~$\R^3$. This class of data is based on
functions which vary slowly in one direction. The idea is that 2-D
inhomogeneous Navier-Stokes system with large data is globally well-posedness
and we construct the 3-D approximate solutions by the 2-D solutions with a
parameter. One of the key point of this study is the investigation of the time
decay properties of the solutions to the 2-D inhomogeneous Navier-Stokes
system. We obtained the same optimal decay estimates as the solutions of 2-D
homogeneous Navier-Stokes system.
