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

doi:10.1002/cpa.22023

CORC > 数学与系统科学研究院 > 中国科学院数学与系统科学研究院 > 应用数学研究所

	On Ill- and Well-Posedness of Dissipative Martingale Solutions to Stochastic 3D Euler Equations
	Hofmanova, Martina 3; Zhu, Rongchan 2; Zhu, Xiangchan 1,4
刊名	COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS
	2021-09-28
页码	65
ISSN号	0010-3640
DOI	10.1002/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
出版者	WILEY
WOS记录号	WOS:000700379000001
内容类型	期刊论文
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.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Beijing Inst Technol, Dept Math, Beijing 100081, Peoples R China 3.Univ Bielefeld, Fak Math, D-33501 Bielefeld, Germany 4.Acad Math & Syst Sci, Beijing, 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.