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

Constantin, 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 doi: 10.1007/s00205-010-0314-x

Abstract/Summary

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.