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.
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机译：本文的目的是提供一大类初始数据，这些数据在整个空间〜$ \ R ^ 3 $中产生3-D非均匀不可压缩Navier-Stokes系统的全局光滑解。此类数据基于在一个方向上缓慢变化的功能。这个想法是，具有大数据的2-D齐次Navier-Stokes系统具有全局良好的适定性，我们用带有参数的2-D解构造了3-D近似解。这项研究的重点之一是研究二维非均匀Navier-Stokes系统解的时间衰减特性。我们获得了与2-均匀Navier-Stokes系统解相同的最佳衰减估计。
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