Acta Mathematica

A geometric approach to generalized Stokes conjectures

Eugen Varvaruca and Georg S. Weiss

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We consider the Stokes conjecture concerning the shape of extreme 2-dimensional water waves. By new geometric methods including a non-linear frequency formula, we prove the Stokes conjecture in the original variables. Our results do not rely on structural assumptions needed in previous results such as isolated singularities, symmetry and monotonicity. Part of our results extends to the mathematical problem in higher dimensions.


Dedicated to John Toland on the occasion of his 60th birthday.

Article information

Acta Math., Volume 206, Number 2 (2011), 363-403.

Received: 13 August 2009
Revised: 27 May 2010
First available in Project Euclid: 31 January 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35R35: Free boundary problems
Secondary: 76B15: Water waves, gravity waves; dispersion and scattering, nonlinear interaction [See also 35Q30] 76B07: Free-surface potential flows

Water wave Stokes conjecture singularity frequency formula concentration compactness

2011 © Institut Mittag-Leffler


Varvaruca, Eugen; Weiss, Georg S. A geometric approach to generalized Stokes conjectures. Acta Math. 206 (2011), no. 2, 363--403. doi:10.1007/s11511-011-0066-y.

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