Overhanging solitary water waves

Juan Davila Bonczos; Manuel Del Pino; Monica Musso; Miles Wheeler

Overhanging solitary water waves

Juan Davila Bonczos, Manuel Del Pino, Monica Musso, Miles Wheeler

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

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, Hélein, and Pacard. The method developed here is related to the construction of constant mean curvature surfaces through gluing.

Original language	English
Journal	Inventiones Mathematicae
Publication status	Acceptance date - 21 Dec 2025

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https://arxiv.org/pdf/2409.01182

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Overhanging Final 25-12-2025 (accepted manuscript)
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Embargo ends: 31/12/99
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title = "Overhanging solitary water waves",

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{\'e}lein, and Pacard. The method developed here is related to the construction of constant mean curvature surfaces through gluing. ",

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T1 - Overhanging solitary water waves

AU - Davila Bonczos, Juan

AU - Del Pino, Manuel

AU - Musso, Monica

AU - Wheeler, Miles

PY - 2025/12/21

Y1 - 2025/12/21

N2 - 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, Hélein, and Pacard. The method developed here is related to the construction of constant mean curvature surfaces through gluing.

AB - 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, Hélein, and Pacard. The method developed here is related to the construction of constant mean curvature surfaces through gluing.

M3 - Article

SN - 0020-9910

JO - Inventiones Mathematicae

JF - Inventiones Mathematicae

ER -

Overhanging solitary water waves

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