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

doi:10.1214/21-AAP1740

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	GLOBAL WELL-POSEDNESS OF THE 3D NAVIER-STOKES EQUATIONS PERTURBED BY A DETERMINISTIC VECTOR FIELD
	Flandoli, Franco 1; Hofmanova, Martina 2; Luo, Dejun3 ; Nilssen, Torstein 4
	2022-08-01
发表期刊	ANNALS OF APPLIED PROBABILITY
ISSN	1050-5164
卷号	32 期号:4 页码:2568-2586
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.
关键词	3D Navier-Stokes equations vorticity form well-posedness regularization by noise Wong-Zakai principle
DOI	10.1214/21-AAP1740
收录类别	SCI
语种	英语
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
WOS类目	Statistics & Probability
WOS记录号	WOS:000842053600006
出版者	INST MATHEMATICAL STATISTICS-IMS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/61088
专题	应用数学研究所
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.