KMS Of Academy of mathematics and systems sciences, CAS
| Stochastic mSQG equations with multiplicative transport noises: White noise solutions and scaling limit | |
Luo, Dejun1,2 ; Zhu, Rongchan3,4
| |
| 2021-10-01 | |
| Source Publication | STOCHASTIC PROCESSES AND THEIR APPLICATIONS
 |
| ISSN | 0304-4149 |
| Volume | 140Pages:236-286 |
| Abstract | 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. |
| Keyword | Modified Surface Quasi-Geostrophic equation Transport noise White noise solution Scaling limit Weak convergence |
| DOI | 10.1016/j.spa.2021.06.013 |
| Indexed By | SCI |
| Language | 英语 |
| WOS Research Area | Mathematics |
| WOS Subject | Statistics & Probability |
| WOS ID | WOS:000690365800009 |
| Publisher | ELSEVIER |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/59166 |
| Collection | 应用数学研究所 |
| Corresponding Author | Zhu, Rongchan |
| Affiliation | 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 |
| Recommended Citation 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. |
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