Three-dimensional steady water waves with vorticity

In recent years there has been a lot of progress on two-dimensional steady water waves with vorticity and three-dimensional waves with zero vorticity (irrotational flow). The three-dimensional case with vorticity remains largely unexplored. Part of the reason is that the problem (generally) doesn't reduce to an elliptic free boundary problem. In my talk I will discuss recent progress on this topic. I will mainly focus on an ongoing work where we consider doubly periodic, symmetric gravity-capillary waves with small vorticity, by treating the problem as elliptic-hyperbolic and using ideas from the theory of magnetohydrostatic equilibria.

This is joint work with D. S. Seth and K. Varholm.

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