Stokes waves with vorticity
Analysis of PDEs
2009-12-02 v3
Abstract
The existence of periodic waves propagating downstream on the surface of a two-dimensional infinitely deep water under gravity is established for a general class of vorticities. When reformulated as an elliptic boundary value problem in a fixed semi-infinite strip with a parameter, the operator describing the problem is nonlinear and non-Fredholm. A global connected set of nontrivial solutions is obtained via singular theory of bifurcation. Each solution on the continuum has a symmetric and monotone wave profile. The proof uses a generalized degree theory, global bifurcation theory and Wyburn's lemma in topology, combined with the Schauder theory for elliptic problems and the maximum principle.
Keywords
Cite
@article{arxiv.0911.5542,
title = {Stokes waves with vorticity},
author = {Vera Mikyoung Hur},
journal= {arXiv preprint arXiv:0911.5542},
year = {2009}
}