Two-component equations modelling water waves with constant vorticity

Joachim Escher; David Henry; Boris Kolev; Tony Lyons

doi:10.1007/s10231-014-0461-z

Two-component equations modelling water waves with constant vorticity

Joachim Escher
, David Henry
, Boris Kolev
, Tony Lyons

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we derive a two-component system of nonlinear equations which models two-dimensional shallow water waves with constant vorticity. Then, we prove well-posedness of this equation using a geometrical framework which allows us to recast this equation as a geodesic flow on an infinite-dimensional manifold. Finally, we provide a criterion for global existence.

Original language	English
Pages (from-to)	249-271
Number of pages	23
Journal	Annali di Matematica Pura ed Applicata
Volume	195
Issue number	1
DOIs	https://doi.org/10.1007/s10231-014-0461-z
Publication status	Published - 1 Feb 2016

Keywords

Diffeomorphism group
Euler equation
Model equations
Vorticity
Water waves

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10.1007/s10231-014-0461-z

https://hdl.handle.net/10468/12168Licence: CC BY-NC-ND

Cite this

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AU - Lyons, Tony

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N2 - In this paper, we derive a two-component system of nonlinear equations which models two-dimensional shallow water waves with constant vorticity. Then, we prove well-posedness of this equation using a geometrical framework which allows us to recast this equation as a geodesic flow on an infinite-dimensional manifold. Finally, we provide a criterion for global existence.

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KW - Diffeomorphism group

KW - Euler equation

KW - Model equations

KW - Vorticity

KW - Water waves

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Two-component equations modelling water waves with constant vorticity

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Keywords

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