Steady water waves with localized vorticity
July 19, 2019 16:30-17:30
曾崇纯 (Georgia Institute of Technology)
We consider the capillary-gravity problem -- the free boundary problem of the Euler equation with gravity and surface tension -- and construct finite energy steady waves with vorticity based on a bifurcation approach. Unlike those perturbed from shear flows, the vorticity of these solutions are highly concentrated, including traveling waves with compactly supported vorticity and smooth stationary waves with rapidly decaying vorticity.