Department of Mathematics - Seminar on PDE - Overhanging solitary water waves

We construct gravity water waves with constant vorticity having the approximate form
of a disk joined to a strip by a thin neck. This is the first rigorous existence result for such
waves, which have been seen in numerics since the 80s and 90s. Our method is related to
the construction of constant mean curvature surfaces through gluing, and 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, Helein, and Pacard. This is joint work with Juan Davila, Manuel del Pino,
and Monica Musso.