English

Survey on periodic vortex patches

Analysis of PDEs 2026-07-14 v1

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.

Cite

@article{arxiv.2607.12577,
  title  = {Survey on periodic vortex patches},
  author = {Claudia García},
  journal= {arXiv preprint arXiv:2607.12577},
  year   = {2026}
}