Global bifurcation of doubly periodic waves in Beltrami flows

Most of the current theory on three-dimensional steady water waves assumes irrotational flow. One exception is the construction of a family of small-amplitude doubly periodic gravity-capillary waves on Beltrami flows by Erik Wahlén, Lokharu and Svensson Seth from 2020. In my talk I will describe a global continuation of this family. One of the challenges is that the local family is constructed using a multiparameter bifurcation approach, whereas global bifurcation theory usually assumes a single bifurcation parameter. Our theory includes irrotational flow as a special case. This is joint work with Bastian Hilder and Erik Wahlén.