Zu Chongzhi Mathematics Research Seminar

Date and Time (China standard time): Tuesday, June 11, 10:00-11:00 am

Location: WDR 1007

Zoom: 953 9322 3574, Passcode: dkumath

Title: Global Bifurcation of Surface Capillary Waves on a 2D Droplet

Speaker: Yilun Wu

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.

Bio: Dr. Wu obtained his Ph.D. from University of Michigan, and did his postdoctoral research at Indiana University and Brown University. He is currently associate professor at University of Oklahoma. Dr. Wu’s research field is analysis of PDE, focusing on existence and stability of steady solutions and solitary waves. The equations he studies involve fluids, kinetic theory, water waves and general relativity. He uses tools from nonlinear elliptic and hyperbolic equations, calculus of variations, spectral theory and bifurcation theory, integrable systems and inverse scattering, and harmonic analysis.