Steady periodic water waves with constant vorticity: regularity and local bifurcation

Details Steady periodic water waves with constant vorticity: regularity and local bifurcation Steady periodic water waves with constant vorticity: regularity and local bifurcation

2009-10-04

arxiv.org/abs/0910.0618v2

Mathematics

Analysis of PDEs

Three new figures added, result in Appendix B improved, several new references added

Scientific paper

This paper studies periodic traveling gravity waves at the free surface of water in a flow of constant vorticity over a flat bed. Using conformal mappings the free-boundary problem is transformed into a quasilinear pseudodifferential equation for a periodic function of one variable. The new formulation leads to a regularity result and, by use of bifurcation theory, to the existence of waves of small amplitude even in the presence of stagnation points in the flow.

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