Abstract
In this paper, we study the vortex patch problem in an ideal fluid in a planar bounded domain. By solving a certain minimization problem and studying the limiting behavior of the minimizer, we prove that for any harmonic function q corresponding to a nontrivial irrotational flow, there exists a family of steady vortex patches approaching the set of extreme points of q on the boundary of the domain. Furthermore, we show that each finite collection of strict extreme points of q corresponds to a family of steady multiple vortex patches approaching it.
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Acknowledgements
The first author was supported by National Natural Science Foundation of China (Grant No. 11331010) and Chinese Academy of Sciences (Grant No. QYZDJ-SSW-SYS021). The second author was supported by National Natural Science Foundation of China (Grant No. 11771469). The authors are grateful to the two anonymous referees for helpful comments.
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Cao, D., Wang, G. & Zhan, W. Steady vortex patches near a nontrivial irrotational flow. Sci. China Math. 64, 947–962 (2021). https://doi.org/10.1007/s11425-018-9495-1
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DOI: https://doi.org/10.1007/s11425-018-9495-1