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},
pages = {1--19},
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/}
}
TY - JOUR AU - Lannes, David TI - Derivation and mathematical analysis of a nonlocal model for large amplitude internal waves JO - Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" N1 - talk:7 PY - 2008-2009 SP - 1 EP - 19 PB - Centre de mathématiques Laurent Schwartz, École polytechnique UR - http://www.numdam.org/item/SEDP_2008-2009____A7_0/ LA - en ID - SEDP_2008-2009____A7_0 ER -
%0 Journal Article %A Lannes, David %T Derivation and mathematical analysis of a nonlocal model for large amplitude internal waves %J Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" %Z talk:7 %D 2008-2009 %P 1-19 %I Centre de mathématiques Laurent Schwartz, École polytechnique %U http://www.numdam.org/item/SEDP_2008-2009____A7_0/ %G en %F SEDP_2008-2009____A7_0
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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