Global bifurcation of steady gravity water waves with critical layers
Analysis of PDEs
2014-07-02 v1
Abstract
We construct large families of two-dimensional travelling water waves propagating under the influence of gravity in a flow of constant vorticity over a flat bed. A Riemann-Hilbert problem approach is used to recast the governing equations as a one-dimensional elliptic pseudo-differential 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.
Keywords
Cite
@article{arxiv.1407.0092,
title = {Global bifurcation of steady gravity water waves with critical layers},
author = {Adrian Constantin and Walter Strauss and Eugen Varvaruca},
journal= {arXiv preprint arXiv:1407.0092},
year = {2014}
}