English

From point vortices to vortex patches in self-similar expanding configurations

Analysis of PDEs 2020-01-03 v2

Abstract

The main result is that given a generic self-similarly expanding configuration of 3 point vortices that start sufficiently far out, we can instead take compactly supported vorticity functions, and the resulting solution to 2D incompressible Euler will evolve like a nearby point vortex configuration for all time, with the size of the patches growing at most as t1/4+ϵt^{1/4+\epsilon} and the distance between them growing as t\sqrt{t}.

Keywords

Cite

@article{arxiv.1912.10862,
  title  = {From point vortices to vortex patches in self-similar expanding configurations},
  author = {Samuel Zbarsky},
  journal= {arXiv preprint arXiv:1912.10862},
  year   = {2020}
}

Comments

Updated and expanded introduction; some fixed typos