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

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:259

Article

Zhu, Rongchan¹  Zhu, Xiangchan² 

[1] Beijing Inst Technol, Dept Math, Beijing 100081, Peoples R China

[2] Beijing Jiaotong Univ, Sch Sci, Beijing 100044, Peoples R China

关键词: Stochastic Navier-Stokes equation;    Regularity structure;    Paracontrolled distribution;    Space-time white noise;    Renormalisation;   

DOI  :  10.1016/j.jde.2015.06.002

来源: Elsevier

【 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, Perkowsld in [12]. We also compare the two approaches. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free