Paper

Asymptotic behaviour of global vortex rings

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Published 17 June 2022 • © 2022 IOP Publishing Ltd & London Mathematical Society
, , Citation Daomin Cao et al 2022 Nonlinearity 35 3680 DOI 10.1088/1361-6544/ac7497

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Author e-mails

dmcao@amt.ac.cn

wanjie@bit.edu.cn

wangguodong@hit.edu.cn

zhanweicheng@amss.ac.cn

Author affiliations

1 Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China

2 University of Chinese Academy of Sciences, Beijing 100049, People's Republic of China

3 School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, People's Republic of China

4 Institute for Advanced Study in Mathematics, Harbin Institute of Technology, Harbin 150001, People's Republic of China

5 School of Mathematical Sciences, Xiamen University, Xiamen 361005, People's Republic of China

Author notes

6 Author to whom any correspondence should be addressed.

7 Recommended by Dr Karima Khusnutdinova.

Dates

  1. Received 13 April 2021
  2. Revised 25 March 2022
  3. Accepted 30 May 2022
  4. Published

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0951-7715/35/7/3680

Abstract

In this paper, we are concerned with nonlinear desingularization of steady vortex rings in ${\mathbb{R}}^{3}$ with a general nonlinearity f. Using the improved vorticity method, we construct a family of steady vortex rings which constitute a desingularization of the classical circular vortex filament in the whole space. The requirements on f are very general, and it may not satisfy the Ambrosetti–Rabinowitz condition. Some qualitative and asymptotic properties are also established.

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Recommended by Dr Karima Khusnutdinova

10.1088/1361-6544/ac7497