# Derivation and mathematical analysis of a nonlocal model for large amplitude internal waves

David Lannes^{[1]}

- [1] École Normale Supérieure DMA et CNRS UMR 8553 45, rue d’Ulm 75005 Paris France

Séminaire Équations aux dérivées partielles (2008-2009)

- Volume: 2008-2009, page 1-19

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topLannes, David. "Derivation and mathematical analysis of a nonlocal model for large amplitude internal waves." Séminaire Équations aux dérivées partielles 2008-2009 (2008-2009): 1-19. <http://eudml.org/doc/11203>.

@article{Lannes2008-2009,

abstract = {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.},

affiliation = {École Normale Supérieure DMA et CNRS UMR 8553 45, rue d’Ulm 75005 Paris France},

author = {Lannes, David},

journal = {Séminaire Équations aux dérivées partielles},

keywords = {shallow-water equations; bi-fluid; Euler equations; well-posedness},

language = {eng},

pages = {1-19},

publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},

title = {Derivation and mathematical analysis of a nonlocal model for large amplitude internal waves},

url = {http://eudml.org/doc/11203},

volume = {2008-2009},

year = {2008-2009},

}

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

PY - 2008-2009

PB - Centre de mathématiques Laurent Schwartz, École polytechnique

VL - 2008-2009

SP - 1

EP - 19

AB - 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.

LA - eng

KW - shallow-water equations; bi-fluid; Euler equations; well-posedness

UR - http://eudml.org/doc/11203

ER -

## References

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