Special Session 95: The Euler Water Wave Problem

Stability and instability of gravity-capillary waves
Erik Wahl\`en
Lund University
Sweden
Co-Author(s):    Mariana Haragus, Wei Lian, Changzhen Sun, Tien Truong
Abstract:
I will report on recent progress on the spectral stability and instability of periodic travelling gravity-capillary waves for the irrotational water wave problem in two space dimensions (one-dimensional surface). This includes both co-periodic, transverse and localised perturbations. I will also discuss some implications for the stability of generalised solitary waves, consisting of a localised hump with periodic ripples in the far field.