Derivation and mathematical analysis of a nonlocal model for large amplitude internal waves
Lannes, David1
1 École Normale Supérieure DMA et CNRS UMR 8553 45, rue d’Ulm 75005 Paris France
Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2008-2009), Exposé no. 7, 19 p.

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This note is devoted to the study of a bi-fluid generalization of the nonlinear shallow-water equations. It describes the evolution of the interface between two fluids of different densities. In the case of a two-dimensional interface, this systems contains unexpected nonlocal terms (that are of course not present in the usual one-fluid shallow water equations). We show here how to derive this systems from the two-fluid Euler equations and then show that it is locally well-posed.

Lannes, David 1

1 École Normale Supérieure DMA et CNRS UMR 8553 45, rue d’Ulm 75005 Paris France 
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Lannes, David. Derivation and mathematical analysis of a nonlocal model for large amplitude internal waves. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2008-2009), Exposé no. 7, 19 p. https://geodesic-test.mathdoc.fr/item/SEDP_2008-2009____A7_0/