Existence of capillary-gravity water waves with piecewise constant vorticity |
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Authors: | Calin Iulian Martin Bogdan-Vasile Matioc |
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Institution: | 1. Institut für Mathematik, Universität Wien, Nordbergstraße 15, 1090 Wien, Austria;2. Institut für Angewandte Mathematik, Leibniz Universität Hannover, Welfengarten 1, 30167 Hannover, Germany |
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Abstract: | In this paper we construct small-amplitude periodic capillary-gravity water waves with a piecewise constant vorticity distribution. They describe water waves traveling on superposed linearly sheared currents that have different vorticities. This is achieved by associating to the height function formulation of the water wave problem a diffraction problem where we impose suitable transmission conditions on each line where the vorticity function has a jump. The solutions of the diffraction problem, found by using local bifurcation theory, are the desired solutions of the hydrodynamical problem. |
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Keywords: | 76B03 76B45 76B70 47J15 |
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