PDEA Seminar: Travelling periodic water waves with vorticity

Abstract: The water wave problem, consisting of the incompressible Euler equations of fluid dynamics in a domain with a free boundary (the water surface), is a centuries-old problem which has attracted the attention of many famous mathematicians. Historically, most research on water waves has been based on the assumption of irrotational flow, but the last decades have seen a lot of progress on waves with vorticity. This is for example useful for modelling wave-current interactions. In my talk I will give an overview of recent analytical work on travelling waves with vorticity, focusing on the periodic situation. In the two-dimensional setting this includes results on large-amplitude gravity waves, where one finds overhanging waves in addition to the classical peaked highest waves which also appear in the irrotational case. The three-dimensional problem is more challenging, but I will describe some existence results obtained in the last years.

This is a seminar in the PDEs and Applications seminar series.