Title: Three-dimensional gravity waves on Beltrami flows

Abstract: 
The existence of doubly periodic gravity waves over an irrotational flow was established by Iooss and Plotnikov in their papers (2009, 2011). The problem is technically demanding due to a small-divisor phenomenon arising in the existence proof, which prevents the direct use of the classical implicit function theorem. Iooss and Plotnikov overcame this difficulty by employing a Nash–Moser theorem.

In this talk, I will explain how their existence result can be extended to Beltrami flows, a class of rotational flows in which the velocity field is parallel to the vorticity. I will highlight the key differences and new challenges that appear in the rotational setting, and give an outline of an existence proof for doubly periodic Beltrami gravity waves.

This talk is based on joint work with Mark Groves, Stefano Pasquali and Erik Wahlén.