A geometric approach to generalized Stokes conjectures

Eugen Varvaruca Department of Mathematics and Statistics, University of Reading Georg S. Weiss Mathematical Institute, Heinrich Heine University

Analysis of PDEs Geometric Modeling and Processing mathscidoc:1701.03003

Acta Mathematica, 206, (2), 363-403, 2009.8
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.
Water wave; Stokes conjecture; singularity; frequency formula; concentration compactness
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  title={A geometric approach to generalized Stokes conjectures},
  author={Eugen Varvaruca, and Georg S. Weiss},
  booktitle={Acta Mathematica},
Eugen Varvaruca, and Georg S. Weiss. A geometric approach to generalized Stokes conjectures. 2009. Vol. 206. In Acta Mathematica. pp.363-403. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203356890244742.
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