Time: 16:00-17:00 June 4, 2024 (Tuesday)
Place: MCM110
Title: Global Bifurcation of Surface Capillary Waves on a 2D Droplet
Abstract: The existence of steady traveling waves bifurcating from a flat surface is a classical problem in water wave theory. The well-known Stokes waves form a global continuum of periodic steady gravity waves which approach a limiting singular solution with a 120$^\circ$ angle at the top. Recently, Dyachenko et al. obtained numerically a branch of rotating traveling wave solutions bifurcating from a circular droplet in 2D. In this talk, we show a rigorous global bifurcation result constructing a set of such solutions. The obtained solutions are steady surface capillary waves in 2D, and have $m$-fold rotational symmetry. This is joint work with Gary Moon.
