# American Institute of Mathematical Sciences

July  2011, 16(1): 361-383. doi: 10.3934/dcdsb.2011.16.361

## Derivation and stability study of a rigid lid bilayer model

 1 Laboratoire d'Analyse Numérique et Informatique, Université Gaston Berger, UFR SAT BP 234 Saint-Louis, Sénégal, LAMA, UMR 5127 CNRS, Université de Savoie, 73376 Le Bourget du lac, France 2 Laboratoire d'Analyse Numérique et d'Informatique (LANI), Université Gaston Berger, BP 234, Saint-Louis

Received  December 2009 Revised  September 2010 Published  April 2011

In this paper we present the derivation of a bilayer shallow water model with rigid lid hypothesis. We start from the incompressible Navier-Stokes equations, we introduce a small parameter $\varepsilon$ which is the ratio between the characteristic height and the characteristic length of the fluids domain. We use a formal asymptotic expansion then we resort to averaging to obtain the model. We also prove the stability of the model, in the following sense, up to a subsequence, every sequence of weak solutions converges to a solution of the model.
Citation: Timack Ngom, Mamadou Sy. Derivation and stability study of a rigid lid bilayer model. Discrete & Continuous Dynamical Systems - B, 2011, 16 (1) : 361-383. doi: 10.3934/dcdsb.2011.16.361
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