January/February 2016 On the strong solutions of the inhomogeneous incompressible Navier-Stokes equations in a thin domain
Xian Liao
Differential Integral Equations 29(1/2): 167-182 (January/February 2016). DOI: 10.57262/die/1448323258

Abstract

In this work, we will show the global existence of the strong solutions of the inhomogeneous incompressible Navier-Stokes equations in a thin three dimensional domain $\Omega=\mathbb R^2\times [0,\epsilon]$, with Dirichlet boundary condition on the top and bottom boundary: the global well-posedness may hold for large initial data when the vertical size $\epsilon$ is sufficiently small. Furthermore, when $\epsilon\rightarrow 0$ the velocity tends to vanish away from the initial time. The analysis relies on the a priori $H^2$-estimate for the solutions (similar as in [4, 5, 21]) and one pays attention to the dependence on the vertical size $\epsilon$.

Citation

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Xian Liao. "On the strong solutions of the inhomogeneous incompressible Navier-Stokes equations in a thin domain." Differential Integral Equations 29 (1/2) 167 - 182, January/February 2016. https://doi.org/10.57262/die/1448323258

Information

Published: January/February 2016
First available in Project Euclid: 24 November 2015

zbMATH: 1363.35276
MathSciNet: MR3450754
Digital Object Identifier: 10.57262/die/1448323258

Subjects:
Primary: 35Q30 , 76D03

Rights: Copyright © 2016 Khayyam Publishing, Inc.

Vol.29 • No. 1/2 • January/February 2016
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