Steady Periodic Water Waves with Constant Vorticity: Regularity and Local Bifurcation |
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Authors: | Adrian Constantin Eugen Varvaruca |
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Affiliation: | 1.Faculty of Mathematics,University of Vienna,Vienna,Austria;2.Department of Mathematics,Imperial College London,London,UK |
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Abstract: | This paper studies periodic traveling gravity waves at the free surface of water in a flow of constant vorticity over a flat bed. Using conformal mappings the free-boundary problem is transformed into a quasilinear pseudodifferential equation for a periodic function of one variable. The new formulation leads to a regularity result and, by use of bifurcation theory, to the existence of waves of small amplitude even in the presence of stagnation points in the flow. |
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