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GLOBAL WELL-POSEDNESS OF THE 3D NAVIER-STOKES EQUATIONS PERTURBED BY A DETERMINISTIC VECTOR FIELD
Flandoli, Franco1; Hofmanova, Martina2; Luo, Dejun3; Nilssen, Torstein4
2022-08-01
Source PublicationANNALS OF APPLIED PROBABILITY
ISSN1050-5164
Volume32Issue:4Pages:2568-2586
AbstractWe 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.
Keyword3D Navier-Stokes equations vorticity form well-posedness regularization by noise Wong-Zakai principle
DOI10.1214/21-AAP1740
Indexed BySCI
Language英语
Funding ProjectGerman 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 Research AreaMathematics
WOS SubjectStatistics & Probability
WOS IDWOS:000842053600006
PublisherINST MATHEMATICAL STATISTICS-IMS
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/61088
Collection应用数学研究所
Corresponding AuthorFlandoli, Franco
Affiliation1.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
Recommended Citation
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.
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