Three-dimensional Navier-Stokes equations driven by space-time white noise

Rongchan Zhu; Xiangchan Zhu

doi:10.1016/j.jde.2015.06.002

Three-dimensional Navier-Stokes equations driven by space-time white noise

Rongchan Zhu, Xiangchan Zhu^*

^*此作品的通讯作者

数学学院

Beijing Jiaotong University

科研成果: 期刊稿件 › 文章 › 同行评审

43 引用（Scopus）

摘要

In this paper we prove existence and uniqueness of local solutions to the three-dimensional (3D) Navier-Stokes (N-S) equation driven by space-time white noise using two methods: first, the theory of regularity structures introduced by Martin Hairer in [16] and second, the paracontrolled distribution proposed by Gubinelli, Imkeller, Perkowski in [12]. We also compare the two approaches.

源语言	英语
页（从-至）	4443-4508
页数	66
期刊	Journal of Differential Equations
卷	259
期	9
DOI	https://doi.org/10.1016/j.jde.2015.06.002
出版状态	已出版 - 5 11月 2015

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Zhu, R., & Zhu, X. (2015). Three-dimensional Navier-Stokes equations driven by space-time white noise. Journal of Differential Equations, 259(9), 4443-4508. https://doi.org/10.1016/j.jde.2015.06.002

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abstract = "In this paper we prove existence and uniqueness of local solutions to the three-dimensional (3D) Navier-Stokes (N-S) equation driven by space-time white noise using two methods: first, the theory of regularity structures introduced by Martin Hairer in [16] and second, the paracontrolled distribution proposed by Gubinelli, Imkeller, Perkowski in [12]. We also compare the two approaches.",

keywords = "Paracontrolled distribution, Regularity structure, Renormalisation, Space-time white noise, Stochastic Navier-Stokes equation",

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AB - In this paper we prove existence and uniqueness of local solutions to the three-dimensional (3D) Navier-Stokes (N-S) equation driven by space-time white noise using two methods: first, the theory of regularity structures introduced by Martin Hairer in [16] and second, the paracontrolled distribution proposed by Gubinelli, Imkeller, Perkowski in [12]. We also compare the two approaches.

KW - Paracontrolled distribution

KW - Regularity structure

KW - Renormalisation

KW - Space-time white noise

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Three-dimensional Navier-Stokes equations driven by space-time white noise

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