Regularity and symmetry properties of rotational solitary water waves |
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Authors: | Anca-Voichita Matioc Bogdan-Vasile Matioc |
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Affiliation: | 1. Institut f??r Mathematik, Universit?t Wien, Nordbergstrasse 15, 1090, Vienna, Austria
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Abstract: | We prove that a solitary water wave driven by gravity has real-analytic streamlines for arbitrary vorticity functions if the flow contains no stagnation points. Based on this property, we show that if all the streamlines attain their global maximum (resp. minimum) on the same vertical line, then the solitary wave has to be symmetric and strictly monotone away from the crest (resp. trough). Our results are true for sub- and supercritical solitary waves as well. |
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