A geometric approach to generalized Stokes conjectures
Varvaruca, E. and Weiss, G. S. (2011) A geometric approach to generalized Stokes conjectures. Acta Mathematica, 206 (2). pp. 363-403. ISSN 1871-2509
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To link to this item DOI: 10.1007/s11511-011-0066-y
We consider the Stokes conjecture concerning the shape of extreme two-dimensional water waves. By new geometric methods including a nonlinear 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.