GLOBAL WELL-POSEDNESS OF THE 3D NAVIER-STOKES EQUATIONS PERTURBED BY A DETERMINISTIC VECTOR FIELD

doi:10.1214/21-AAP1740

	GLOBAL WELL-POSEDNESS OF THE 3D NAVIER-STOKES EQUATIONS PERTURBED BY A DETERMINISTIC VECTOR FIELD
	Flandoli, Franco 1; Hofmanova, Martina 2; Luo, Dejun 3; Nilssen, Torstein 4
刊名	ANNALS OF APPLIED PROBABILITY
	2022-08-01
卷号	32 期号:4 页码:2568-2586
关键词	3D Navier-Stokes equations vorticity form well-posedness regularization by noise Wong-Zakai principle
ISSN号	1050-5164
DOI	10.1214/21-AAP1740
英文摘要	We are concerned with the problem of global well-posedness of the 3D Navier-Stokes equations on the torus with unitary viscosity. While a full answer to this question seems to be out of reach of the current techniques, we establish a regularization by a deterministic vector field. More precisely, we consider the vorticity form of the system perturbed by an additional transport type term. Such a perturbation conserves the enstrophy and therefore a priori it does not imply any smoothing. Our main result is a construction of a deterministic vector field v = v(t, x) which provides the desired regularization of the system and yields global well-posedness for large initial data outside arbitrary small sets. The proof relies on probabilistic arguments developed by Flandoli and Luo, tools from rough path theory by Hofmanova, Leahy and Nilssen and a new Wong-Zakai approximation result, which itself combines probabilistic and rough path techniques.
资助项目	German Science Foundation DFG[SFB 1283] ; German Science Foundation DFG[FOR 2402] ; European Research Council (ERC) under the European Union[949981] ; National Key R&D Program of China[2020YFA0712700] ; National Natural Science Foundation of China[11688101] ; National Natural Science Foundation of China[11931004] ; National Natural Science Foundation of China[12090014] ; Youth Innovation Promotion Association, CAS[2017003]
WOS研究方向	Mathematics
语种	英语
出版者	INST MATHEMATICAL STATISTICS-IMS
WOS记录号	WOS:000842053600006
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/61087]
专题	中国科学院数学与系统科学研究院
通讯作者	Flandoli, Franco
作者单位	1.Scuola Normale Super Pisa, Classe Sci, Pisa, Italy 2.Univ Bielefeld, Fak Math, Bielefeld, Germany 3.Chinese Acad Sci, Acad Math & Syst Sci, Beijing, Peoples R China 4.Univ Agder, Inst Math, Kristiansand, Norway
推荐引用方式 GB/T 7714	Flandoli, Franco,Hofmanova, Martina,Luo, Dejun,et al. GLOBAL WELL-POSEDNESS OF THE 3D NAVIER-STOKES EQUATIONS PERTURBED BY A DETERMINISTIC VECTOR FIELD[J]. ANNALS OF APPLIED PROBABILITY,2022,32(4):2568-2586.
APA	Flandoli, Franco,Hofmanova, Martina,Luo, Dejun,&Nilssen, Torstein.(2022).GLOBAL WELL-POSEDNESS OF THE 3D NAVIER-STOKES EQUATIONS PERTURBED BY A DETERMINISTIC VECTOR FIELD.ANNALS OF APPLIED PROBABILITY,32(4),2568-2586.
MLA	Flandoli, Franco,et al."GLOBAL WELL-POSEDNESS OF THE 3D NAVIER-STOKES EQUATIONS PERTURBED BY A DETERMINISTIC VECTOR FIELD".ANNALS OF APPLIED PROBABILITY 32.4(2022):2568-2586.