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On Ill- and Well-Posedness of Dissipative Martingale Solutions to Stochastic 3D Euler Equations

文献类型：期刊论文

作者Hofmanova, Martina1; Zhu, Rongchan2; Zhu, Xiangchan3,4
刊名COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS
出版日期2021-09-28
页码65
ISSN号0010-3640
DOI10.1002/cpa.22023
英文摘要We are concerned with the question of well-posedness of stochastic, three-dimensional, incompressible Euler equations. In particular, we introduce a novel class of dissipative solutions and show that (i) existence; (ii) weak-strong uniqueness; (iii) nonuniqueness in law; (iv) existence of a strong Markov solution; (v) nonuniqueness of strong Markov solutions: all hold true within this class. Moreover, as a by-product of (iii) we obtain existence and nonuniqueness of probabilistically strong and analytically weak solutions defined up to a stopping time and satisfying an energy inequality. (c) 2021 Wiley Periodicals LLC.
资助项目European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme[949981] ; DFG[CRC 1283] ; NSFC[11922103] ; NSFC[11771037] ; NSFC[12090014] ; NSFC[11688101] ; National Key R&D Program of China[2020YFA0712700] ; key Lab of Random Complex Structures and Data Science, Youth Innovation Promotion Association, Chinese Academy of Science[2020003]
WOS研究方向Mathematics
语种英语
WOS记录号WOS:000700379000001
出版者WILEY
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/59362]  
专题应用数学研究所
通讯作者Hofmanova, Martina
作者单位1.Univ Bielefeld, Fak Math, D-33501 Bielefeld, Germany
2.Beijing Inst Technol, Dept Math, Beijing 100081, Peoples R China
3.Acad Math & Syst Sci, Beijing, Peoples R China
4.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
推荐引用方式
GB/T 7714		 Hofmanova, Martina,Zhu, Rongchan,Zhu, Xiangchan. On Ill- and Well-Posedness of Dissipative Martingale Solutions to Stochastic 3D Euler Equations[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS,2021:65.
APA Hofmanova, Martina,Zhu, Rongchan,&Zhu, Xiangchan.(2021).On Ill- and Well-Posedness of Dissipative Martingale Solutions to Stochastic 3D Euler Equations.COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS,65.
MLA Hofmanova, Martina,et al."On Ill- and Well-Posedness of Dissipative Martingale Solutions to Stochastic 3D Euler Equations".COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS (2021):65.

入库方式： OAI收割

来源：数学与系统科学研究院

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