REGULARIZATION OF PLANAR VORTICES FOR THE INCOMPRESSIBLE FLOW

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	REGULARIZATION OF PLANAR VORTICES FOR THE INCOMPRESSIBLE FLOW
	Cao, Daomin1 ; Peng, Shuangjie 2,3; Yan, Shusen 4
刊名	ACTA MATHEMATICA SCIENTIA
	2018-09-01
卷号	38 期号:5 页码:1443-1467
关键词	regularization planar vortices vorticity sets reduction
ISSN号	0252-9602
英文摘要	In this paper, we continue to construct stationary classical solutions for the incompressible planar flows approximating singular stationary solutions of this problem. This procedure is carried out by constructing solutions for the following elliptic equations {- Delta u = lambda Sigma(k)(j=1) 1(B delta(x0, j)) (u- k(j))(+)(p), in Omega, u = 0 on partial derivative Omega, where 0 < p < 1, Omega subset of R-2 is a bounded simply-connected smooth domain, k(i) (i = 1,..., k) is prescribed positive constant. The result we prove is that for any given non-degenerate critical point x(0) = (x(0,1),..., x(0,k)) of the Kirchhoff-Routh function defined on Omega(k) corresponding to (k(1), ..., k(k)), there exists a stationary classical solution approximating stationary k points vortex solution. Moreover, as lambda ->+infinity, the vorticity set {y : u(lambda) > k(j)} boolean AND B-delta(X-0,X-j) shrinks to {x(0,j)}, and the local vorticity strength near each x(0,j) approaches k(j), j = 1,..., k. This result makes the study of the above problem with p >= 0 complete since the cases p > 1, p = 1, p = 0 have already been studied in [11, 12] and [13] respectively.
WOS研究方向	Mathematics
语种	英语
出版者	ELSEVIER SCIENCE INC
WOS记录号	WOS:000446808900002
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/31351]
专题	应用数学研究所
通讯作者	Cao, Daomin
作者单位	1.Chinese Acad Sci, Inst Appl Math, Beijing 100190, Peoples R China 2.Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China 3.Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Hubei, Peoples R China 4.Univ New England Armidale, Dept Math, Armidale, NSW 2351, Australia
推荐引用方式 GB/T 7714	Cao, Daomin,Peng, Shuangjie,Yan, Shusen. REGULARIZATION OF PLANAR VORTICES FOR THE INCOMPRESSIBLE FLOW[J]. ACTA MATHEMATICA SCIENTIA,2018,38(5):1443-1467.
APA	Cao, Daomin,Peng, Shuangjie,&Yan, Shusen.(2018).REGULARIZATION OF PLANAR VORTICES FOR THE INCOMPRESSIBLE FLOW.ACTA MATHEMATICA SCIENTIA,38(5),1443-1467.
MLA	Cao, Daomin,et al."REGULARIZATION OF PLANAR VORTICES FOR THE INCOMPRESSIBLE FLOW".ACTA MATHEMATICA SCIENTIA 38.5(2018):1443-1467.