Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Steady periodic waves bifurcating for fixed-depth rotational flows

Author: David Henry
Journal: Quart. Appl. Math. 71 (2013), 455-487
MSC (2010): Primary 35B32, 35Q31, 35J25
DOI: https://doi.org/10.1090/S0033-569X-2013-01293-8
Published electronically: May 16, 2013
MathSciNet review: 3112823
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Abstract: We consider steady periodic water waves for rotational flows with a specified fixed depth over a flat bed. We construct a modified height function, which explicitly introduces the mean depth into the rotational water wave problem, and use the Crandall-Rabinowitz local bifurcation theorem to establish the existence of solutions of the resulting problem.

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Additional Information

David Henry
Affiliation: School of Mathematical Sciences, Dublin City University, Glasnevin, Dublin 9, Ireland
Email: david.henry@dcu.ie

DOI: https://doi.org/10.1090/S0033-569X-2013-01293-8
Keywords: Local-bifurcation, steady periodic waves, vorticity, fixed-depth flows.
Received by editor(s): June 26, 2011
Published electronically: May 16, 2013
Article copyright: © Copyright 2013 Brown University