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The purpose of this paper is to provide a large class of initial data whichgenerates global smooth solution of the 3-D inhomogeneous incompressibleNavier-Stokes system in the whole space~$\R^3$. This class of data is based onfunctions which vary slowly in one direction. The idea is that 2-Dinhomogeneous Navier-Stokes system with large data is globally well-posednessand we construct the 3-D approximate solutions by the 2-D solutions with aparameter. One of the key point of this study is the investigation of the timedecay properties of the solutions to the 2-D inhomogeneous Navier-Stokessystem. We obtained the same optimal decay estimates as the solutions of 2-Dhomogeneous Navier-Stokes system.

Inhomogeneous incompressible viscous flows with slowly varying initial data