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 MULTISCALE STEADY VORTEX PATCHES FOR 2D INCOMPRESSIBLE EULER EQUATIONS Cao, Daomin1,2; Wan, Jie3 2022 Source Publication SIAM JOURNAL ON MATHEMATICAL ANALYSIS ISSN 0036-1410 Volume 54Issue:2Pages:1488-1514 Abstract In this paper, we study the existence and qualitative properties of multiscale steady vortex patches for Euler equations in a 2D bounded domain. By considering certain maximization problems for the vorticity, we obtain the existence of double vortex patches which are trapped in a neighborhood of two points. Limiting localizations of these two points are determined by the Robin function and the boundary of the domain, rather than critical points of the Kirchhoff--Routh function H2, which is quite different from all the known results. Moreover, the strengths of two components of vorticity are of different order. Multiscale vortex patches concentrating near k points are also constructed for any integer k \geq 2. Keyword steady vortex patch desingularization Kirchhoff--Routh function Robin function variational method DOI 10.1137/21M1390529 Indexed By SCI Language 英语 Funding Project National Natural Science Foun-dation of China[11831009] ; Chinese Academy of Sciences[QYZDJ-SSW-SYS021] ; National Natural Science Foundation of China[12101045] ; Beijing Institute of Technology Research Fund Program for Young Scholars[3170011182016] WOS Research Area Mathematics WOS Subject Mathematics, Applied WOS ID WOS:000797597300006 Publisher SIAM PUBLICATIONS Citation statistics Document Type 期刊论文 Identifier http://ir.amss.ac.cn/handle/2S8OKBNM/61352 Collection 应用数学研究所 Corresponding Author Cao, Daomin Affiliation 1.Chinese Acad Sci, Inst Appl Math, Beijing 100190, Peoples R China2.Univ Chinese Acad Sci, Beijing 100049, Peoples R China3.Beijing Inst Technol, Sch Math & Stat, Beijing 100081, Peoples R China Recommended CitationGB/T 7714 Cao, Daomin,Wan, Jie. MULTISCALE STEADY VORTEX PATCHES FOR 2D INCOMPRESSIBLE EULER EQUATIONS[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS,2022,54(2):1488-1514. APA Cao, Daomin,&Wan, Jie.(2022).MULTISCALE STEADY VORTEX PATCHES FOR 2D INCOMPRESSIBLE EULER EQUATIONS.SIAM JOURNAL ON MATHEMATICAL ANALYSIS,54(2),1488-1514. MLA Cao, Daomin,et al."MULTISCALE STEADY VORTEX PATCHES FOR 2D INCOMPRESSIBLE EULER EQUATIONS".SIAM JOURNAL ON MATHEMATICAL ANALYSIS 54.2(2022):1488-1514.
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