Differential and Integral Equations

On the symmetry of periodic gravity water waves with vorticity

Anca-Voichita Matioc and Bogdan-Vasile Matioc

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We study the a priori symmetry of periodic gravity water waves with arbitrarily many crests and troughs, and general vorticity distributions. We show that if all the streamlines achieve their global minimum on the same vertical line, then the wave has exactly one trough and crest within a period, and is symmetric with respect to the vertical line containing the crest.

Article information

Differential Integral Equations, Volume 26, Number 1/2 (2013), 129-140.

First available in Project Euclid: 18 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 76B15: Water waves, gravity waves; dispersion and scattering, nonlinear interaction [See also 35Q30] 76B47: Vortex flows 35B50: Maximum principles 26E05: Real-analytic functions [See also 32B05, 32C05]


Matioc, Anca-Voichita; Matioc, Bogdan-Vasile. On the symmetry of periodic gravity water waves with vorticity. Differential Integral Equations 26 (2013), no. 1/2, 129--140. https://projecteuclid.org/euclid.die/1355867510

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