Special Session 56: Dynamical properties of nonlinear partial differential equations

Three-dimensional doubly periodic gravity water waves on Beltrami flows
Erik Wahl\`en
Lund University
Sweden
Co-Author(s):    Mark Groves, Dag Nilsson, Stefano Pasquali
Abstract:
I will present an existence result for small-amplitude doubly periodic travelling gravity water waves on Beltrami flows, a class of rotational flows in which the velocity field is parallel to the vorticity. This extends the existence theory by Iooss and Plotnikov in the irrotational setting. The problem is technically challenging due to the appearance of small divisors. We overcome this by using a Nash--Moser theorem. I will highlight the key differences and new issues that appear in the Beltrami setting.