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INHOMOGENEOUS INCOMPRESSIBLE VISCOUS FLOWS WITH SLOWLY VARYING INITIAL DATA
- Part of
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- Journal:
- Journal of the Institute of Mathematics of Jussieu / Volume 17 / Issue 5 / November 2018
- Published online by Cambridge University Press:
- 03 November 2016, pp. 1121-1172
- Print publication:
- November 2018
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- Article
- Export citation
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The purpose of this paper is to provide a large class of initial data which generates global smooth solution of the 3D inhomogeneous incompressible Navier–Stokes system in the whole space
$\mathbb{R}^{3}$. This class of data is based on functions which vary slowly in one direction. The idea is that 2D inhomogeneous Navier–Stokes system with large data is globally well-posed and we construct the 3D approximate solutions by the 2D 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 2D inhomogeneous Navier–Stokes system. We obtained the same optimal decay estimates as the solutions of 2D homogeneous Navier–Stokes system.
