Constantin and Iyer's Representation Formula for the Navier-Stokes Equations on Manifolds

doi:10.1007/s11118-017-9631-0

CSpace > 应用数学研究所

	Constantin and Iyer's Representation Formula for the Navier-Stokes Equations on Manifolds
	Fang, Shizan 1; Luo, Dejun2,3
	2018-02-01
发表期刊	POTENTIAL ANALYSIS
ISSN	0926-2601
卷号	48 期号:2 页码:181-206
摘要	The 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.
关键词	Navier-Stokes equations Stochastic representation de Rham-Hodge Laplacian Stochastic flow Pull-back vector field
DOI	10.1007/s11118-017-9631-0
语种	英语
资助项目	National 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研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000422968600003
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/29355
专题	应用数学研究所
通讯作者	Luo, Dejun
作者单位	1.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
推荐引用方式 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.