Approximations of stochastic 3D tamed Navier-Stokes equations

Xuhui Peng; Rangrang Zhang

doi:10.3934/cpaa.2020241

Article Contents

2020, Volume 19, Issue 12: 5337-5365. Doi: 10.3934/cpaa.2020241

This issue Previous Article Large deviation theorems for dirichlet determinants of analytic quasi-periodic jacobi operators with Brjuno-Rüssmann frequency Next Article Limiting behavior of non-autonomous stochastic reaction-diffusion equations with colored noise on unbounded thin domains

Approximations of stochastic 3D tamed Navier-Stokes equations

Xuhui Peng^1, and
Rangrang Zhang^2, ,

1.
MOE-LCSM, School of Mathematics and Statistics, Hunan Normal University, Hunan, 410081, China
2.
School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 100081, China

^* Corresponding author
^* Corresponding author

Received: December 31, 2019

Revised: June 30, 2020

Early access: September 2020

Published: December 2020

This work was supported by NSFC (No. 11801032, 11971227, 11501195, 11871476). Hunan Provincial Natural Science Foundation of China (No. 2019JJ50377). Key Laboratory of Random Complex Structures and Data Science, Academy of Mathematics and Systems Science, CAS (No. 2008DP173182). Beijing Institute of Technology Research Fund Program for Young Scholars. The Construct Program of the Key Discipline in Hunan Province

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In this paper, we are concerned with 3D tamed Navier-Stokes equations with periodic boundary conditions, which can be viewed as an approximation of the classical 3D Navier-Stokes equations. We show that the strong solution of 3D tamed Navier-Stokes equations driven by Poisson random measure converges weakly to the strong solution of 3D tamed Navier-Stokes equations driven by Gaussian noise on the state space $ \mathcal{D}([0, T];\mathbb{H}^1) $.

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Mathematics Subject Classification: Primary: 60H15; Secondary: 93E20, 35R60.

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