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rho-White noise solution to 2D stochastic Euler equations

文献类型：期刊论文

作者Flandoli, Franco3; Luo, Dejun1,2
刊名PROBABILITY THEORY AND RELATED FIELDS
出版日期2019-12-01
卷号175期号:3-4页码:783-832
关键词White noise 2D Euler equations Multiplicative noise Fokker-Planck equation Gradient estimates
ISSN号0178-8051
DOI10.1007/s00440-019-00902-8
英文摘要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.
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
语种英语
WOS记录号WOS:000493683800004
出版者SPRINGER HEIDELBERG
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/50627]  
专题应用数学研究所
通讯作者Flandoli, Franco
作者单位1.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, RCSDS, Beijing 100190, Peoples R China
3.Scuola Normale Super Pisa, Pisa, Italy
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.

入库方式： OAI收割

来源：数学与系统科学研究院

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