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.

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.

@article{SEDP_2008-2009____A7_0,
     author = {Lannes, David},
     title = {Derivation and mathematical analysis of a nonlocal model for large amplitude internal waves},
     journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"},
     note = {talk:7},
     publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
     year = {2008-2009},
     language = {en},
     url = {http://www.numdam.org/item/SEDP_2008-2009____A7_0/}
}
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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. http://www.numdam.org/item/SEDP_2008-2009____A7_0/

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