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2016 Global bifurcation of steady gravity water waves with critical layers
Adrian Constantin, Walter Strauss, Eugen Vărvărucă
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Acta Math. 217(2): 195-262 (2016). DOI: 10.1007/s11511-017-0144-x


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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Adrian Constantin. Walter Strauss. Eugen Vărvărucă. "Global bifurcation of steady gravity water waves with critical layers." Acta Math. 217 (2) 195 - 262, 2016.


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

zbMATH: 1375.35294
MathSciNet: MR3689941
Digital Object Identifier: 10.1007/s11511-017-0144-x

Rights: 2016 © Institut Mittag-Leffler

Vol.217 • No. 2 • 2016
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