Videos

[Moved Online] Connections Workshop: Mathematical Problems In Fluid Dynamics - Unstable water waves: periodic Evans function approach

Presenter
January 20, 2021
Abstract
I will discuss spectral instability of a Stokes wave of small amplitude in the finite depth. Analysis of a periodic Evans function, which is new, near the origin of the spectral plane offers an alternative proof of the Benjamin-Feir instability. Analysis near the resonance of order 2 reveals spectral instability when 0.86430...1.3627..., so new unstable waves are found. This seems the first rigorous proof of such high-frequency instability. I will discuss extensions to capillary-gravity waves and others, if time permits. Joint work with Z. Yang.