Differential and Integral Equations

On the analyticity of periodic gravity water waves with integrable vorticity function

Joachim Escher and Bogdan-Vasile Matioc

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We prove that the streamlines and the profile of periodic gravity water waves traveling over a flat bed with wavespeed which exceeds the horizontal velocity of all fluid particles are real-analytic graphs if the vorticity function is merely integrable.

Article information

Differential Integral Equations, Volume 27, Number 3/4 (2014), 217-232.

First available in Project Euclid: 30 January 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35Q31: Euler equations [See also 76D05, 76D07, 76N10] 76B03: Existence, uniqueness, and regularity theory [See also 35Q35] 76B15: Water waves, gravity waves; dispersion and scattering, nonlinear interaction [See also 35Q30] 76B47: Vortex flows


Escher, Joachim; Matioc, Bogdan-Vasile. On the analyticity of periodic gravity water waves with integrable vorticity function. Differential Integral Equations 27 (2014), no. 3/4, 217--232. https://projecteuclid.org/euclid.die/1391091364

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