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

By Adrian Constantin and Eugen Varvaruca


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
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