Asymptotic analysis for the 3D primitive equations in a channel

Makram Hamouda; Chang-Yeol Jung; Roger Temam

doi:10.3934/dcdss.2013.6.401

Article Contents

2013, Volume 6, Issue 2: 401-422. Doi: 10.3934/dcdss.2013.6.401

This issue Previous Article A Cahn-Hilliard-Gurtin model with dynamic boundary conditions Next Article Parabolic quasi-variational diffusion problems with gradient constraints

Asymptotic analysis for the 3D primitive equations in a channel

1.
The Institute for Scientific Computing and Applied Mathematics, Indiana University, 831 E. 3rd St., Rawles Hall, Bloomington, IN 47405
2.
School of Technology Management/ Mechanical, and Advanced Materials Engineering/ Natural Science, Ulsan National Institute of Science and Technology, San 194, Banyeon-ri, Eonyang-eup, Ulju-gun, Ulsan

Received: July 2011

Revised: November 2011

Published: April 2013

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Abstract

In this article, we give an asymptotic expansion, with respect to the viscosity which is considered here to be small, of the solutions of the $3D$ linearized Primitive Equations (EPs) in a channel with lateral periodicity. A rigorous convergence result, in some physically relevant space, is proven. This allows, among other consequences, to confirm the natural choice of the non-local boundary conditions for the non-viscous PEs.

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Mathematics Subject Classification: 35B25, 35C20, 76D05, 76N20.

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