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Exact periodic traveling water waves with vorticity. (English) Zbl 1020.35012

Summary: For the classical inviscid water wave problem under the influence of gravity, described by the Euler equation with a free surface over a flat bottom, we construct periodic traveling waves with vorticity. They are symmetric waves whose profiles are monotone between each crest and trough. We use global bifurcation theory to construct a connected set of such solutions. This set contains flat waves as well as waves that approach flows with stagnation points.

MSC:

35B35 Stability in context of PDEs
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
35Q35 PDEs in connection with fluid mechanics
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