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

  • Mateusz KluczekEmail author
  • Adrián Rodríguez-Sanjurjo
Part of the Tutorials, Schools, and Workshops in the Mathematical Sciences book series (TSWMS)


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.


Global diffeomorphism Geophysical internal water waves Exact and explicit solution 

Mathematics Subject Classification (2000)

35A16 35C05 35Q86 35Q35 



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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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversity College CorkCorkIreland

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