DESINGULARIZATION OF VORTICES FOR TWO-DIMENSIONAL STEADY EULER FLOWS VIA THE VORTICITY METHOD

doi:10.1137/19M1292151

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	DESINGULARIZATION OF VORTICES FOR TWO-DIMENSIONAL STEADY EULER FLOWS VIA THE VORTICITY METHOD
	Cao, Daomin 2,3; Wang, Guodong 1; Zhan, Weicheng 2,3
刊名	SIAM JOURNAL ON MATHEMATICAL ANALYSIS
	2020
卷号	52 期号:6 页码:5363-5388
关键词	desingularization of vortices 2D Euler flow vorticity method nonlinear stability
ISSN号	0036-1410
DOI	10.1137/19M1292151
英文摘要	In this paper, we consider steady Euler flows in a planar bounded domain in which the vorticity is sharply concentrated in a finite number of disjoint regions of small diameter. Such flows are closely related to the point vortex model and can be regarded as desingularization of point vortices. By an adaption of the vorticity method, we construct a family of steady Euler flows in which the vorticity is concentrated near a global minimum point of the Robin function of the domain, and the corresponding stream function satisfies a semilinear elliptic equation with a given profile function. Furthermore, for any given isolated minimum point (x(1), ..., x(k)) of the Kirchhoff-Routh function of the domain, we prove that there exists a family of steady Euler flows whose vorticity is supported in k small regions near x(i), and near each x(i) the corresponding stream function satisfies a semilinear elliptic equation with a given profile function.
资助项目	NNSF of China[12001135] ; NNSF of China[11831009] ; China Postdoctoral Science Foundation[2019M661261]
WOS研究方向	Mathematics
语种	英语
出版者	SIAM PUBLICATIONS
WOS记录号	WOS:000600695200002
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/57876]
专题	应用数学研究所
通讯作者	Wang, Guodong
作者单位	1.Harbin Inst Technol, Inst Adv Study Math, Harbin 150001, Peoples R China 2.Chinese Acad Sci, Inst Appl Math, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Cao, Daomin,Wang, Guodong,Zhan, Weicheng. DESINGULARIZATION OF VORTICES FOR TWO-DIMENSIONAL STEADY EULER FLOWS VIA THE VORTICITY METHOD[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS,2020,52(6):5363-5388.
APA	Cao, Daomin,Wang, Guodong,&Zhan, Weicheng.(2020).DESINGULARIZATION OF VORTICES FOR TWO-DIMENSIONAL STEADY EULER FLOWS VIA THE VORTICITY METHOD.SIAM JOURNAL ON MATHEMATICAL ANALYSIS,52(6),5363-5388.
MLA	Cao, Daomin,et al."DESINGULARIZATION OF VORTICES FOR TWO-DIMENSIONAL STEADY EULER FLOWS VIA THE VORTICITY METHOD".SIAM JOURNAL ON MATHEMATICAL ANALYSIS 52.6(2020):5363-5388.