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, Daomin1,2 ; Wang, Guodong 3; Zhan, Weicheng 1,2
	2020
发表期刊	SIAM JOURNAL ON MATHEMATICAL ANALYSIS
ISSN	0036-1410
卷号	52 期号:6 页码:5363-5388
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.
关键词	desingularization of vortices 2D Euler flow vorticity method nonlinear stability
DOI	10.1137/19M1292151
收录类别	SCI
语种	英语
资助项目	NNSF of China[12001135] ; NNSF of China[11831009] ; China Postdoctoral Science Foundation[2019M661261]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000600695200002
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/57877
专题	应用数学研究所
通讯作者	Wang, Guodong
作者单位	1.Chinese Acad Sci, Inst Appl Math, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Beijing 100049, Peoples R China 3.Harbin Inst Technol, Inst Adv Study Math, Harbin 150001, 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.