Stochastic mSQG equations with multiplicative transport noises: White noise solutions and scaling limit

doi:10.1016/j.spa.2021.06.013

CSpace > 应用数学研究所

	Stochastic mSQG equations with multiplicative transport noises: White noise solutions and scaling limit
	Luo, Dejun1,2 ; Zhu, Rongchan 3,4
	2021-10-01
发表期刊	STOCHASTIC PROCESSES AND THEIR APPLICATIONS
ISSN	0304-4149
卷号	140 页码:236-286
摘要	We consider the modified Surface Quasi-Geostrophic (mSQG) equation on the 2D torus T-2, perturbed by multiplicative transport noise. The equation admits the white noise measure on T-2 as the invariant measure. We first prove the existence of white noise solutions to the stochastic equation via the method of point vortex approximation, then, under a suitable scaling limit of the noise, we show that the solutions converge weakly to the unique stationary solution of the dissipative mSQG equation driven by spacetime white noise. The weak uniqueness of the latter equation is also proved by following Gubinelli and Perkowski's approach in Gubinelli and Perkowski (2020). (C) 2021 Elsevier B.V. All rights reserved.
关键词	Modified Surface Quasi-Geostrophic equation Transport noise White noise solution Scaling limit Weak convergence
DOI	10.1016/j.spa.2021.06.013
收录类别	SCI
语种	英语
WOS研究方向	Mathematics
WOS类目	Statistics & Probability
WOS记录号	WOS:000690365800009
出版者	ELSEVIER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/59166
专题	应用数学研究所
通讯作者	Zhu, Rongchan
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab RCSDS, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Beijing Inst Technol, Dept Math, Beijing 100081, Peoples R China 4.Univ Bielefeld, Dept Math, D-33615 Bielefeld, Germany
推荐引用方式 GB/T 7714	Luo, Dejun,Zhu, Rongchan. Stochastic mSQG equations with multiplicative transport noises: White noise solutions and scaling limit[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS,2021,140:236-286.
APA	Luo, Dejun,&Zhu, Rongchan.(2021).Stochastic mSQG equations with multiplicative transport noises: White noise solutions and scaling limit.STOCHASTIC PROCESSES AND THEIR APPLICATIONS,140,236-286.
MLA	Luo, Dejun,et al."Stochastic mSQG equations with multiplicative transport noises: White noise solutions and scaling limit".STOCHASTIC PROCESSES AND THEIR APPLICATIONS 140(2021):236-286.