Three-dimensional water waves

Abstract: The other talks in the series have concentrated on two-dimensional water waves. In my talk I will give an overview of the considerably younger three-dimensional theory. In the irrotational case, there is by now a rich existence theory for small-amplitude solutions. These can have different behaviours in different horizontal directions, e.g. periodic or solitary. In the talk I will mainly focus on waves which are "doubly periodic", that is, periodic in two different horizontal directions, or "fully localised", that is, solitary in all horizontal directions. As we will see, surface tension plays a much more crucial role than in 2D. I will also discuss some recent work on 3D water waves with vorticity.

analysis of PDEsclassical analysis and ODEs

Audience: researchers in the topic

Online Northeast PDE and Analysis Seminar