KMS Of Academy of mathematics and systems sciences, CAS
PLANAR VORTICES IN A BOUNDED DOMAIN WITH A HOLE | |
Yan, Shusen1; Yu, Weilin2 | |
2021-12-01 | |
Source Publication | ELECTRONIC RESEARCH ARCHIVE |
Volume | 29Issue:6Pages:4229-4241 |
Abstract | 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. |
Keyword | The Euler flow semilinear elliptic equation variational method free boundary problem reduction |
DOI | 10.3934/era.2021081 |
Indexed By | SCI |
Language | 英语 |
WOS Research Area | Mathematics |
WOS Subject | Mathematics |
WOS ID | WOS:000719684200030 |
Publisher | AMER INST MATHEMATICAL SCIENCES-AIMS |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/59596 |
Collection | 中国科学院数学与系统科学研究院 |
Corresponding Author | Yan, Shusen |
Affiliation | 1.Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China 2.Chinese Acad Sci, Inst Appl Math, Beijing 100190, Peoples R China |
Recommended Citation 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. |
Files in This Item: | ||||||
There are no files associated with this item. |
Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.
Edit Comment