Acta Mathematica

Global bifurcation of steady gravity water waves with critical layers

Adrian Constantin, Walter Strauss, and Eugen Vărvărucă

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We construct families of two-dimensional travelling water waves propagating under the influence of gravity in a flow of constant vorticity over a flat bed, in particular establishing the existence of waves of large amplitude. A Riemann–Hilbert problem approach is used to recast the governing equations as a one-dimensional elliptic pseudodifferential equation with a scalar constraint. The structural properties of this formulation, which arises as the Euler–Lagrange equation of an energy functional, enable us to develop a theory of analytic global bifurcation.

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Acta Math., Volume 217, Number 2 (2016), 195-262.

Received: 30 June 2014
Revised: 26 February 2016
First available in Project Euclid: 17 August 2017

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2016 © Institut Mittag-Leffler


Constantin, Adrian; Strauss, Walter; Vărvărucă, Eugen. Global bifurcation of steady gravity water waves with critical layers. Acta Math. 217 (2016), no. 2, 195--262. doi:10.1007/s11511-017-0144-x.

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