English

Existence of co-rotating and travelling vortex patches with doubly connected components for active scalar equations

Analysis of PDEs 2021-04-05 v2

Abstract

By applying implicit function theorem on contour dynamics, we prove the existence of co-rotating and travelling patch solutions for both Euler and the generalized surface quasi-geostrophic equation. The solutions obtained constitute a desingularization of points vortices when the size of patch support vanishes. In particular, solutions constructed in this paper consist of doubly connected components, which is essentially different from all known results.

Keywords

Cite

@article{arxiv.2103.04328,
  title  = {Existence of co-rotating and travelling vortex patches with doubly connected components for active scalar equations},
  author = {Daomin Cao and Guolin Qin and Weicheng Zhan and Changjun Zou},
  journal= {arXiv preprint arXiv:2103.04328},
  year   = {2021}
}