A geometric approach to generalized Stokes conjectures

• 成果类型: Article
• 署名作者: Varvaruca, Eugen; Weiss, Georg S.
• 署名单位: University of Reading; Heinrich Heine University Dusseldorf
• 刊物名称: ACTA MATHEMATICA
• ISSN/ISSBN: 0001-5962
• DOI: 10.1007/s11511-011-0066-y
• 发表日期: 2011
• 页码: 363-403
• 关键词: periodic water-waves; free-boundary; gravity-waves; PARTIAL REGULARITY; WEAK SOLUTIONS; EXISTENCE

摘要

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.