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Steady periodic water waves with constant vorticity: regularity and local bifurcation\ud \ud

By Adrian Constantin and Eugen Varvaruca

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. \u

Publisher: Springer Verlag (Germany)
Year: 2011
OAI identifier: oai:centaur.reading.ac.uk:17527
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  • http://dx.doi.org/10.1007/s002... (external link)
  • http://arxiv.org/abs/0910.0618... (external link)
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