rho-White noise solution to 2D stochastic Euler equations

doi:10.1007/s00440-019-00902-8

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	rho-White noise solution to 2D stochastic Euler equations
	Flandoli, Franco 1; Luo, Dejun2,3
	2019-12-01
发表期刊	PROBABILITY THEORY AND RELATED FIELDS
ISSN	0178-8051
卷号	175 期号:3-4 页码:783-832
摘要	A stochastic version of 2D Euler equations with transport type noise in the vorticity is considered, in the framework of Albeverio-Cruzeiro theory (Commun Math Phys 129:431-444, 1990) where the equation is considered with random initial conditions related to the so called enstrophy measure. The equation is studied by an approximation scheme based on random point vortices. Stochastic processes solving the Euler equations are constructed and their density with respect to the enstrophy measure is proved to satisfy a Fokker-Planck equation in weak form. Relevant in comparison with the case without noise is the fact that here we prove a gradient type estimate for the density. Although we cannot prove uniqueness for the Fokker-Planck equation, we discuss how the gradient type estimate may be related to this open problem.
关键词	White noise 2D Euler equations Multiplicative noise Fokker-Planck equation Gradient estimates
DOI	10.1007/s00440-019-00902-8
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China[11571347] ; National Natural Science Foundation of China[11688101] ; Special Talent Program of the Academy of Mathematics and Systems Science, Chinese Academy of Sciences
WOS研究方向	Mathematics
WOS类目	Statistics & Probability
WOS记录号	WOS:000493683800004
出版者	SPRINGER HEIDELBERG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/50628
专题	应用数学研究所
通讯作者	Flandoli, Franco
作者单位	1.Scuola Normale Super Pisa, Pisa, Italy 2.Chinese Acad Sci, Acad Math & Syst Sci, RCSDS, 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	Flandoli, Franco,Luo, Dejun. rho-White noise solution to 2D stochastic Euler equations[J]. PROBABILITY THEORY AND RELATED FIELDS,2019,175(3-4):783-832.
APA	Flandoli, Franco,&Luo, Dejun.(2019).rho-White noise solution to 2D stochastic Euler equations.PROBABILITY THEORY AND RELATED FIELDS,175(3-4),783-832.
MLA	Flandoli, Franco,et al."rho-White noise solution to 2D stochastic Euler equations".PROBABILITY THEORY AND RELATED FIELDS 175.3-4(2019):783-832.