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Nonlinear Water Waves pp 19–34Cite as

Birkhäuser

Global Diffeomorphism of the Lagrangian Flow-map for a Pollard-like Internal Water Wave

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Abstract

In this article we provide an overview of a rigorous justification of the global validity of the fluid motion described by a new exact and explicit solution prescribed in terms of Lagrangian variables of the nonlinear geophysical equations. More precisely, the three-dimensional Lagrangian flow-map describing this exact and explicit solution is proven to be a global diffeomorphism from the labelling domain into the fluid domain. Then, the flow motion is shown to be dynamically possible.

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Acknowledgements

The authors acknowledge the support of the Erwin Schrödinger International Institute for Mathematics and Physics (ESI) during the program “Mathematical Aspects of Physical Oceanography” and the support of the Science Foundation Ireland (SFI) research grant 13/CDA/2117.

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Authors and Affiliations

  1. School of Mathematical Sciences, University College Cork, Cork, Ireland

    Mateusz Kluczek & Adrián Rodríguez-Sanjurjo

Authors
  1. Mateusz Kluczek
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  2. Adrián Rodríguez-Sanjurjo
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Corresponding author

Correspondence to Mateusz Kluczek .

Editor information

Editors and Affiliations

  1. School of Mathematical Sciences, University College Cork, Cork, Ireland

    David Henry

  2. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK

    Konstantinos Kalimeris

  3. School of Mathematics, University of East Anglia, Norwich, UK

    Emilian I. Părău

  4. Department of Mathematics, University College London, London, UK

    Jean-Marc Vanden-Broeck

  5. Centre for Mathematical Sciences, Lund University, Lund, Sweden

    Erik Wahlén

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Kluczek, M., Rodríguez-Sanjurjo, A. (2019). Global Diffeomorphism of the Lagrangian Flow-map for a Pollard-like Internal Water Wave. In: Henry, D., Kalimeris, K., Părău, E., Vanden-Broeck, JM., Wahlén, E. (eds) Nonlinear Water Waves . Tutorials, Schools, and Workshops in the Mathematical Sciences . Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-33536-6_2

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