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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Abstract

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

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

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1355867510

Mathematical Reviews number (MathSciNet)
MR3058701

Zentralblatt MATH identifier
1289.76009

Subjects
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]

Citation

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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