KMS Of Academy of mathematics and systems sciences, CAS
REGULARIZATION OF PLANAR VORTICES FOR THE INCOMPRESSIBLE FLOW | |
Cao, Daomin1; Peng, Shuangjie2,3; Yan, Shusen4 | |
2018-09-01 | |
Source Publication | ACTA MATHEMATICA SCIENTIA |
ISSN | 0252-9602 |
Volume | 38Issue:5Pages:1443-1467 |
Abstract | 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. |
Keyword | regularization planar vortices vorticity sets reduction |
Language | 英语 |
WOS Research Area | Mathematics |
WOS Subject | Mathematics |
WOS ID | WOS:000446808900002 |
Publisher | ELSEVIER SCIENCE INC |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/31352 |
Collection | 应用数学研究所 |
Affiliation | 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 |
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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