标题： 悬垂孤立水波 显示英文标题

标题： Overhanging solitary water waves

摘要： 我们提供了第一个悬垂重力水波的构造，其近似形式为通过一个细颈连接的圆盘和条带。 这些波是孤立波，具有恒定的涡量，并且当适当的无量纲重力常数$g>0$足够小时存在。 我们的构造涉及结合三个相关问题的显式解：一个在刚性旋转中的流体圆盘，一个条带中的线性剪切流，以及Hauswirth、Hélein和Pacard发现的一个特殊区域的缩放版本\cite{hauswirth-helein-pacard}。 这里开发的方法与通过粘合构造常平均曲率曲面的方法有关。 显示英文摘要

摘要： 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.