Acta Mathematica

A geometric approach to generalized Stokes conjectures

Eugen Varvaruca and Georg S. Weiss

Full-text: Open access

Abstract

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.

Dedication

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

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.acta/1485892550

Digital Object Identifier
doi:10.1007/s11511-011-0066-y

Mathematical Reviews number (MathSciNet)
MR2810856

Zentralblatt MATH identifier
1238.35194

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

Keywords
Water wave Stokes conjecture singularity frequency formula concentration compactness

Rights
2011 © Institut Mittag-Leffler

Citation

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. https://projecteuclid.org/euclid.acta/1485892550


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