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Local uniqueness for vortex patch problem in incompressible planar steady flow
Cao, Daomin1,2; Guo, Yuxia3; Peng, Shuangjie4,5; Yan, Shusen4
2019-11-01
Source PublicationJOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES
ISSN0021-7824
Volume131Pages:251-289
AbstractWe investigate a steady planar flow of an ideal fluid in a bounded simply connected domain and focus on the vortex patch problem with prescribed vorticity strength. There are two methods to deal with the existence of solutions for this problem: the vorticity method and the stream function method. A long standing open problem is whether these two entirely different methods result in the same solution. In this paper, we will give a positive answer to this problem by studying the local uniqueness of the solutions. Another result obtained in this paper is that if the domain is convex, then the vortex patch problem has a unique solution. (C) 2019 Elsevier Masson SAS. All rights reserved.
KeywordUniqueness Vortex parch Steady solutions Euler equation
DOI10.1016/j.matpur.2019.05.011
Indexed BySCI
Language英语
Funding ProjectNNSF of China[11629101] ; Chinese Academy of Sciences[QYZDJSSW-SYS021]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000496337800009
PublisherELSEVIER
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/50616
Collection应用数学研究所
Corresponding AuthorCao, Daomin
Affiliation1.Chinese Acad Sci, Inst Appl Math, AMSS, Beijing 100190, Peoples R China
2.Univ Chinese Acad Sci, Beijing 100049, Peoples R China
3.Tsinghua Univ, Dept Math Sci, Beijing, Peoples R China
4.Cent China Normal Univ, Sch Math & Stat, Wuhan, Hubei, Peoples R China
5.Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan, Hubei, Peoples R China
Recommended Citation
GB/T 7714
Cao, Daomin,Guo, Yuxia,Peng, Shuangjie,et al. Local uniqueness for vortex patch problem in incompressible planar steady flow[J]. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES,2019,131:251-289.
APA Cao, Daomin,Guo, Yuxia,Peng, Shuangjie,&Yan, Shusen.(2019).Local uniqueness for vortex patch problem in incompressible planar steady flow.JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES,131,251-289.
MLA Cao, Daomin,et al."Local uniqueness for vortex patch problem in incompressible planar steady flow".JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES 131(2019):251-289.
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