Survey on periodic vortex patches

Abstract

This survey revisits classical results on the existence of periodic solutions in incompressible fluid dynamics. Owing to the breadth of the subject, we restrict our attention to the simplest and most illustrative framework: the two-dimensional Euler equations and vortex patch solutions. The aim is not to present new results, but rather to provide a unified and streamlined exposition of several classical constructions by combining ideas from the original works with more recent developments.