KMS Of Academy of mathematics and systems sciences, CAS
rho-White noise solution to 2D stochastic Euler equations | |
Flandoli, Franco1; Luo, Dejun2,3 | |
2019-12-01 | |
Source Publication | PROBABILITY THEORY AND RELATED FIELDS |
ISSN | 0178-8051 |
Volume | 175Issue:3-4Pages:783-832 |
Abstract | 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. |
Keyword | White noise 2D Euler equations Multiplicative noise Fokker-Planck equation Gradient estimates |
DOI | 10.1007/s00440-019-00902-8 |
Indexed By | SCI |
Language | 英语 |
Funding Project | 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 Research Area | Mathematics |
WOS Subject | Statistics & Probability |
WOS ID | WOS:000493683800004 |
Publisher | SPRINGER HEIDELBERG |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/50628 |
Collection | 应用数学研究所 |
Corresponding Author | Flandoli, Franco |
Affiliation | 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 |
Recommended Citation 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. |
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