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rho-White noise solution to 2D stochastic Euler equations
Flandoli, Franco1; Luo, Dejun2,3
AbstractA 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.
KeywordWhite noise 2D Euler equations Multiplicative noise Fokker-Planck equation Gradient estimates
Indexed BySCI
Funding ProjectNational 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 AreaMathematics
WOS SubjectStatistics & Probability
WOS IDWOS:000493683800004
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Document Type期刊论文
Corresponding AuthorFlandoli, Franco
Affiliation1.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.
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