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A note on steady vortex flows in two dimensions


Authors: Daomin Cao and Guodong Wang
Journal: Proc. Amer. Math. Soc. 148 (2020), 1153-1159
MSC (2010): Primary 33C55, 33C50, 42B15, 42C10
DOI: https://doi.org/10.1090/proc/14776
Published electronically: September 20, 2019
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Abstract: In this note, we give a general criterion for steady vortex flows in a planar bounded domain. More specifically, we show that if the stream function satisfies ``locally'' a semilinear elliptic equation with monotone or Lipschitz nonlinearity, then the flow must be steady.


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Additional Information

Daomin Cao
Affiliation: School of Mathematics and Information Science, Guangzhou University, Guangzhou 510405, People’s Republic of China; and Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China
Email: dmcao@amt.ac.cn

Guodong Wang
Affiliation: Institute for Advanced Study in Mathematics, Harbin Institute of Technology, Harbin 150001, People’s Republic of China
Email: wangguodong14@mails.ucas.ac.cn

DOI: https://doi.org/10.1090/proc/14776
Keywords: Euler equations, steady vortex flow, semilinear elliptic equation, stream function
Received by editor(s): June 9, 2019
Received by editor(s) in revised form: July 9, 2019
Published electronically: September 20, 2019
Additional Notes: The first author was supported by NNSF of China Grant (No. 11831009) and Chinese Academy of Sciences by Grant QYZDJ-SSW-SYS021
The second author was supported by NNSF of China Grant (No.11771469)
The second author is the corresponding author.
Communicated by: Wenxian Shen
Article copyright: © Copyright 2019 American Mathematical Society