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Overhanging solitary water waves

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arxiv 2409.01182 v1 pith:IYPLKA3G submitted 2024-09-02 math.AP

Juan Dávila , Manuel del Pino , Monica Musso , Miles H. Wheeler This is my paper · ORCID
classification math.AP
keywords constantconstructionwavesdiskoverhangingrelatedsolitarystrip
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Large-amplitude periodic solutions to the steady Euler equations with piecewise constant vorticity

    math.AP 2025-06 conditional novelty 8.0 of 10

    A new local elliptic formulation for two-layer constant-vorticity Euler flows yields global bifurcation curves that terminate exactly when conformal equivalence or non-stagnation on the interface breaks down.

  2. From KP-I Lump Solution to Travelling wave of 3D Gravity Capillary Water wave problem

    math.AP 2025-09 conditional novelty 6.0 of 10

    For strong surface tension, the 3D gravity capillary water wave equations admit small fully localized traveling solitary waves whose leading-order profile is a KP-I lump.

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