On the symmetry of periodic gravity water waves with vorticity. (English) Zbl 1289.76009

The paper deals with planar and periodic water waves traveling at the surface of an inviscid fluid when gravity is the predominant extremal force acting on the fluid. Existence of a vertical line where the all streamlines take their global minimum and monotonicity of the wave profile near this line but just on one side of it are required. The authors prove, that there exists a minimal period such that the wave has within this period exactly one crest and is symmetric with respect to the vertical line containing the crest. Moreover, the wave is monotone on either side of the crest.


76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76B47 Vortex flows for incompressible inviscid fluids
35B50 Maximum principles in context of PDEs
26E05 Real-analytic functions
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