Steady periodic water waves with constant vorticity: regularity and local bifurcationConstantin, A. and Varvaruca, E. (2011) Steady periodic water waves with constant vorticity: regularity and local bifurcation. Archive for Rational Mechanics and Analysis, 199 (1). pp. 33-67. ISSN 0003-9527 Full text not archived in this repository. It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing. To link to this item DOI: 10.1007/s00205-010-0314-x Abstract/SummaryThis 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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