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REGULARIZATION OF PLANAR VORTICES FOR THE INCOMPRESSIBLE FLOW
Cao, Daomin1; Peng, Shuangjie2,3; Yan, Shusen4
2018-09-01
Source PublicationACTA MATHEMATICA SCIENTIA
ISSN0252-9602
Volume38Issue:5Pages:1443-1467
AbstractIn 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.
Keywordregularization planar vortices vorticity sets reduction
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000446808900002
PublisherELSEVIER SCIENCE INC
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/31352
Collection应用数学研究所
Affiliation1.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
Recommended Citation
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.
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