Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



On the regularity of deep-water waves with general vorticity distributions

Author: Bogdan-Vasile Matioc
Journal: Quart. Appl. Math. 70 (2012), 393-405
MSC (2010): Primary 35J25, 76B03, 76B47
DOI: https://doi.org/10.1090/S0033-569X-2012-01261-1
Published electronically: March 1, 2012
MathSciNet review: 2953110
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Abstract: We prove that the streamlines and the profile of traveling deep-water waves with Hölder continuous vorticity function are smooth, provided there are no stagnation points in the flow. In addition, if the vorticity function is real analytic, then so is the profile of both solitary and periodic traveling deep-water waves. Finally, by choosing appropriate weighted Sobolev spaces, we show that the streamlines beneath the surface of a periodic traveling water wave are in fact real analytic, provided the vorticity function is merely integrable against a cubic weight.

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Bogdan-Vasile Matioc
Affiliation: Institut für Angewandte Mathematik, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany
Email: matioc@ifam.uni-hannover.de

DOI: https://doi.org/10.1090/S0033-569X-2012-01261-1
Keywords: Deep-water waves, streamlines, vorticity
Received by editor(s): November 17, 2010
Published electronically: March 1, 2012
Article copyright: © Copyright 2012 Brown University

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