Approximating 3D Navier–Stokes equations driven by space-time white noise-Reference-Cited by-同舟云学术

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

Published:2017-12 Issue:04 Volume:20 Page:1750020
ISSN:0219-0257
Container-title:Infinite Dimensional Analysis, Quantum Probability and Related Topics
language:en
Short-container-title:Infin. Dimens. Anal. Quantum. Probab. Relat. Top.

Author:

Zhu Rongchan¹,Zhu Xiangchan²

Affiliation:

1. Department of Mathematics, Beijing Institute of Technology, Beijing 100081, P. R. China

2. School of Science, Beijing Jiaotong University, Beijing 100044, P. R. China

Abstract

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Mathematical Physics,Statistics and Probability,Statistical and Nonlinear Physics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219025717500205

Reference23 articles.

1. Fourier Analysis and Nonlinear Partial Differential Equations

2. Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires

3. Two-Dimensional Navier–Stokes Equations Driven by a Space–Time White Noise

4. Ergodicity for the 3D stochastic Navier–Stokes equations

5. Stochastic Burgers' equation

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