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Constantin and Iyer's Representation Formula for the Navier-Stokes Equations on Manifolds
Fang, Shizan1; Luo, Dejun2,3
2018-02-01
Source PublicationPOTENTIAL ANALYSIS
ISSN0926-2601
Volume48Issue:2Pages:181-206
AbstractThe purpose of this paper is to establish a probabilistic representation formula for the Navier-Stokes equations on compact Riemannian manifolds. Such a formula has been provided by Constantin and Iyer in the flat case of a"e (n) or of T (n) . On a Riemannian manifold, however, there are several different choices of Laplacian operators acting on vector fields. In this paper, we shall use the de Rham-Hodge Laplacian operator which seems more relevant to the probabilistic setting, and adopt Elworthy-Le Jan-Li's idea to decompose it as a sum of the square of Lie derivatives.
KeywordNavier-Stokes equations Stochastic representation de Rham-Hodge Laplacian Stochastic flow Pull-back vector field
DOI10.1007/s11118-017-9631-0
Language英语
Funding ProjectNational Natural Science Foundation of China[11431014] ; National Natural Science Foundation of China[11571347] ; Seven Main Directions[Y129161ZZ1] ; Academy of Mathematics and Systems Science, Chinese Academy of Sciences
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000422968600003
PublisherSPRINGER
Citation statistics
Cited Times:1[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/29355
Collection应用数学研究所
Affiliation1.Univ Bourgogne, IMB, BP 47870, F-21078 Dijon, France
2.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Random Complex Struct & Data Sci, Beijing 100190, Peoples R China
3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
Recommended Citation
GB/T 7714
Fang, Shizan,Luo, Dejun. Constantin and Iyer's Representation Formula for the Navier-Stokes Equations on Manifolds[J]. POTENTIAL ANALYSIS,2018,48(2):181-206.
APA Fang, Shizan,&Luo, Dejun.(2018).Constantin and Iyer's Representation Formula for the Navier-Stokes Equations on Manifolds.POTENTIAL ANALYSIS,48(2),181-206.
MLA Fang, Shizan,et al."Constantin and Iyer's Representation Formula for the Navier-Stokes Equations on Manifolds".POTENTIAL ANALYSIS 48.2(2018):181-206.
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