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Global bifurcation of steady gravity water waves with critical layers

Adrian Constantin King’s College London Walter Strauss Brown University Eugen Varv ˘ aruc ˘ a University of Vienna

Mathematical Physics mathscidoc:1911.43039

Acta Mathematica, 217, (2), 195-262, 2016
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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@inproceedings{adrian2016global,
  title={Global bifurcation of steady gravity water waves with critical layers},
  author={Adrian Constantin, Walter Strauss, and Eugen Varv ˘ aruc ˘ a},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191128152157747594550},
  booktitle={Acta Mathematica},
  volume={217},
  number={2},
  pages={195-262},
  year={2016},
}
Adrian Constantin, Walter Strauss, and Eugen Varv ˘ aruc ˘ a. Global bifurcation of steady gravity water waves with critical layers. 2016. Vol. 217. In Acta Mathematica. pp.195-262. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191128152157747594550.
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