Differential and Integral Equations

On the strong solutions of the inhomogeneous incompressible Navier-Stokes equations in a thin domain

Xian Liao

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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 $\epsilon$.

Article information

Source
Differential Integral Equations Volume 29, Number 1/2 (2016), 167-182.

Dates
First available in Project Euclid: 24 November 2015

Permanent link to this document
https://projecteuclid.org/euclid.die/1448323258

Mathematical Reviews number (MathSciNet)
MR3450754

Zentralblatt MATH identifier
06562172

Subjects
Primary: 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10] 76D03: Existence, uniqueness, and regularity theory [See also 35Q30]

Citation

Liao, Xian. On the strong solutions of the inhomogeneous incompressible Navier-Stokes equations in a thin domain. Differential Integral Equations 29 (2016), no. 1/2, 167--182. https://projecteuclid.org/euclid.die/1448323258.


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