GLOBAL WELL-POSEDNESS OF THE 3D NAVIER-STOKES EQUATIONS PERTURBED BY A DETERMINISTIC VECTOR FIELD
文献类型：期刊论文
| 作者 | Flandoli, Franco1; Hofmanova, Martina2; Luo, Dejun3 ; Nilssen, Torstein4
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| 刊名 | ANNALS OF APPLIED PROBABILITY
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| 出版日期 | 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 |
| WOS记录号 | WOS:000842053600006 |
| 出版者 | INST MATHEMATICAL STATISTICS-IMS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/61087]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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