On Finiteness of Stationary Configurations of the Planar Five-vortex Problem
Mathematical Physics
2025-05-01 v2 Dynamical Systems
math.MP
Abstract
The finiteness problem of stationary configurations for the planar five-vortex problem is considered in this paper. The numbers of equilibria and rigidly translating configurations are shown to be at most 6 and 24 respectively. The numbers of relative equilibria and collapse configurations are shown to be finite, except perhaps if the 5-tuple of vorticities belongs to a given codimension 2 subvariety of the vorticity space. In particular, if the vorticities are of the same sign, the number of stationary configurations is finite.
Keywords
Cite
@article{arxiv.2103.11975,
title = {On Finiteness of Stationary Configurations of the Planar Five-vortex Problem},
author = {Xiang Yu and Shuqiang Zhu},
journal= {arXiv preprint arXiv:2103.11975},
year = {2025}
}
Comments
47 pages, 24 figures. arXiv admin note: text overlap with arXiv:2103.06037