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Derivation and stability study of a rigid lid bilayer model

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  • 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.
    Mathematics Subject Classification: Primary: 35Q35, 35Q30; Secondary: 35B35.


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