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Global bifurcation of steady gravity water waves with constant vorticity

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NWWW01 - Nonlinear water waves

We consider the problem of two-dimensional travelling water waves propagating under the influence of gravity in a flow of constant vorticity over a flat bed. By using a conformal mapping from a strip onto the fluid domain, the governing equations are recasted as a one-dimensional pseudodifferential equation that generalizes Babenko's equation for irrotational waves of infinite depth. We show how an application of the theory of global bifurcation in the real-analytic setting leads to the existence of families of waves of large amplitude that may have critical layers and/or overhanging profiles. This is joint work with Adrian Constantin and Walter Strauss.

This talk is part of the Isaac Newton Institute Seminar Series series.

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