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Annali di Matematica Pura ed Applicata (1923 -)

, Volume 195, Issue 1, pp 249–271 | Cite as

Two-component equations modelling water waves with constant vorticity

  • Joachim Escher
  • David HenryEmail author
  • Boris Kolev
  • Tony Lyons
Article

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.

Keywords

Water waves Vorticity Model equations Euler equation Diffeomorphism group 

Mathematics Subject Classification

35Q35 76B15 35Q53 58D05 

Notes

Acknowledgments

D. Henry, B. Kolev and T. Lyons were supported by the Irish Research Council–Campus France PHC “Ulysses” programme. All the authors would like to thank Rossen Ivanov for his stimulating discussions, and Cathy and Michel for their kind hospitality at Les Grandes Molières during the preparation of this work. The authors would like to thank the anonymous referee for helpful suggestions and comments.

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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Joachim Escher
    • 1
  • David Henry
    • 2
    Email author
  • Boris Kolev
    • 3
  • Tony Lyons
    • 4
  1. 1.Institute for Applied MathematicsUniversity of HanoverHannoverGermany
  2. 2.Department of Applied MathematicsUniversity College CorkCorkIreland
  3. 3.CNRS, Centrale Marseille, I2M, UMR 7373Aix Marseille UniversitéMarseilleFrance
  4. 4.School of Mathematical SciencesDublin Institute of TechnologyDublin 8Ireland

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