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arXiv · 2409.01182

Overhanging solitary water waves

Juan Dávila·Manuel del Pino·Monica Musso·Miles H. Wheeler
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Abstract

We provide the first construction of overhanging gravity water waves having the approximate form of a disk joined to a strip by a thin neck. The waves are solitary with constant vorticity, and exist when an appropriate dimensionless gravitational constant $g>0$ is sufficiently small. Our construction involves combining three explicit solutions to related problems: a disk of fluid in rigid rotation, a linear shear flow in a strip, and a rescaled version of an exceptional domain discovered by Hauswirth, H\'elein, and Pacard \cite{hauswirth-helein-pacard}. The method developed here is related to the construction of constant mean curvature surfaces through gluing.

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Juan Dávila, Manuel del Pino, Monica Musso, Miles H. Wheeler. 2024-09-02. Overhanging solitary water waves. https://arxiv.org/abs/2409.01182

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