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^*

^*Corresponding author for this work

School of Mathematics and Statistics

Beijing Jiaotong University

Research output: Contribution to journal › Article › peer-review

46 Citations (Scopus)

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.

Original language	English
Pages (from-to)	4443-4508
Number of pages	66
Journal	Journal of Differential Equations
Volume	259
Issue number	9
DOIs	https://doi.org/10.1016/j.jde.2015.06.002
Publication status	Published - 5 Nov 2015

Keywords

Paracontrolled distribution
Regularity structure
Renormalisation
Space-time white noise
Stochastic Navier-Stokes equation

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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

KW - Stochastic Navier-Stokes equation

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JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 9

ER -

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

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Keywords

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