Interface boundary value problem for the Navier-Stokes equations in thin two-layer domains
type: Item
instance of: scholarly article
title: Interface boundary value problem for the Navier-Stokes equations in thin two-layer domains
zbMATH Open document ID: 1078.35084
author: I. D. Chueshov
author: Andrey M. Rekalo
author: Geneviève Raugel
published in: Journal of Differential Equations
publication date: 2005-02-22T00:00:00Z
review text: The authors consider the Navier-Stokes equations in a thin two-layer domain \(\Omega_\varepsilon= \Gamma\times (0,\varepsilon)\cup \Gamma\times(-\varepsilon, 0)\), where \(\Gamma= (0,l_1)\times (0,l_2)\subset \mathbb{R}^2\). On the interface \(\Gamma\times \{0\}\), conditions are imposed which essentially how that there is no interaction between the fluids in vertical direction. The authors prove the global existence of strong solutions for large initial data and external forces (the size of which is related to \(\varepsilon\)). The system can be seen as a simplified model for atmosphere-ocean interaction.
reviewed by: Klaus Deckelnick
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 86A05
Mathematics Subject Classification ID: 86A10
Mathematics Subject Classification ID: 37L30
zbMATH DE Number: 2136541
zbMATH Keywords: Navier-Stokes equations
zbMATH Keywords: Thin domains
zbMATH Keywords: Interface conditions
zbMATH Keywords: Global strong solutions
zbMATH Keywords: Spectral decomposition
zbMATH Keywords: Attractors
MaRDI profile type: Publication
full work available at URL: j.jde.2004.03.023
OpenAlex ID: W2018697994
cites work: Large-eigenvalue global existence and regularity results for the Navier-Stokes equation
cites work: Q5394920
cites work: Global attractor of a contact parabolic problem in a thin two-layer domain
cites work: Q4040820
cites work: Q3826993
cites work: Reaction-diffusion equation on thin domains
cites work: A Damped Hyperbolic Equation on Thin Domains
cites work: Q3974735
cites work: The primitive equations on the large scale ocean under the small depth hypothesis.
cites work: The 3D navier-stokes equations seen as a perturbation of the 2D navier-stokes equations
cites work: Some results on the Navier-Stokes equations in thin 3D domains
cites work: Q5526485
cites work: Q5634306
cites work: Mathematical theory for the coupled atmosphere-ocean models (CAO III)
cites work: Asymptotic analysis of the Navier-Stokes equations in thin domains
cites work: Q4242044
cites work: Q3199050
cites work: Navier-Stokes Equations on Thin 3D Domains. I: Global Attractors and Global Regularity of Solutions
cites work: Q4288494
cites work: Q4066072
cites work: Asymptotic behavior of solutions of nonlinear parabolic equations on two-layer thin domains
cites work: Q3873786
cites work: Global attractors for the three-dimensional Navier-Stokes equations
cites work: Some analytic and geometric properties of the solutions of the evolution Navier-Stokes equations
cites work: Q2738697
cites work: Navier-Stokes equations in three-dimensional thin domains with various boundary conditions
cites work: Q4362954
DOI: 10.1016/J.JDE.2004.03.023
description: scientific article; zbMATH DE number 2136541