PLANAR VORTICES IN A BOUNDED DOMAIN WITH A HOLE

doi:10.3934/era.2021081

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	PLANAR VORTICES IN A BOUNDED DOMAIN WITH A HOLE
	Yan, Shusen 1; Yu, Weilin 2
	2021-12-01
发表期刊	ELECTRONIC RESEARCH ARCHIVE
卷号	29 期号:6 页码:4229-4241
摘要	In this paper, we consider the inviscid, incompressible planar flows in a bounded domain with a hole and construct stationary classical solutions with single vortex core, which is closed to the hole. This is carried out by constructing solutions to the following semilinear elliptic problem { -Delta psi = lambda(psi - kappa/4 pi ln lambda)(+)(p), in Omega, psi = rho(lambda), on partial derivative O-0, (1) psi = 0, on partial derivative Omega(0), where p > 1, kappa is a positive constant, rho(lambda) is a constant, depending on lambda, Omega = Omega(0) \ O over line 0 and Omega(0), O-0 are two planar bounded simply-connected domains. We show that under the assumption (ln lambda)Sigma < rho(lambda) < (ln lambda)(1-sigma) for some sigma > 0 small, (1) has a solution psi(lambda), whose vorticity set {y is an element of Omega : psi(y)-kappa+rho(lambda)eta(y) > 0} shrinks to the boundary of the hole as lambda -> +infinity.
关键词	The Euler flow semilinear elliptic equation variational method free boundary problem reduction
DOI	10.3934/era.2021081
收录类别	SCI
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000719684200030
出版者	AMER INST MATHEMATICAL SCIENCES-AIMS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/59596
专题	中国科学院数学与系统科学研究院
通讯作者	Yan, Shusen
作者单位	1.Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China 2.Chinese Acad Sci, Inst Appl Math, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Yan, Shusen,Yu, Weilin. PLANAR VORTICES IN A BOUNDED DOMAIN WITH A HOLE[J]. ELECTRONIC RESEARCH ARCHIVE,2021,29(6):4229-4241.
APA	Yan, Shusen,&Yu, Weilin.(2021).PLANAR VORTICES IN A BOUNDED DOMAIN WITH A HOLE.ELECTRONIC RESEARCH ARCHIVE,29(6),4229-4241.
MLA	Yan, Shusen,et al."PLANAR VORTICES IN A BOUNDED DOMAIN WITH A HOLE".ELECTRONIC RESEARCH ARCHIVE 29.6(2021):4229-4241.