Approximating 3D Navier-Stokes equations driven by space-time white noise

被引：7

作者：

Zhu, Rongchan ^{[1
]}

Zhu, Xiangchan ^{[2
]}

机构：

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

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

来源：

INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS | 2017年 / 20卷 / 04期

关键词：

Stochastic Navier-Stokes equation; regularity structure; paracontrolled distribution; space-time white noise; renormalization; PARTIAL-DIFFERENTIAL-EQUATIONS; LATTICE APPROXIMATIONS; MULTIPLICATIVE NOISE; ERGODICITY;

D O I：

10.1142/S0219025717500205

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study approximations to 3D Navier-Stokes (NS) equation driven by space-time white noise by paracontrolled distribution proposed in Ref. 13. A solution theory for this equation has been developed recently in Ref. 27 based on regularity structure theory and paracontrolled distribution. In order to make the approximating equation converge to 3D NS equation driven by space-time white noise, we should subtract some drift terms in approximating equations. These drift terms, which come from renormalizations in the solution theory, converge to the solution multiplied by some constant depending on approximations.

引用

页数：77

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