Survey on periodic vortex patches
arXiv:2607.12577
summary
The paper surveys classical results on the existence of periodic vortex patch solutions for the two‑dimensional incompressible Euler equations, presenting a unified exposition of earlier constructions and recent developments.
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.
Topics & keywords
#vortex patches#periodic solutions#2d euler equations#incompressible fluid dynamics#mathematical surveyEuler equationsvortex patchperiodic vortexincompressible flowclassical constructions