Asymptotic behavior of random Navier-Stokes equations driven by Wong-Zakai approximations

Anhui Gu; Kening Lu; Bixiang Wang

doi:10.3934/dcds.2019008

Article Contents

2019, Volume 39, Issue 1: 185-218. Doi: 10.3934/dcds.2019008

This issue Previous Article Convexity preserving properties for Hamilton-Jacobi equations in geodesic spaces Next Article Asymptotic behavior in time of solution to the nonlinear Schrödinger equation with higher order anisotropic dispersion

Asymptotic behavior of random Navier-Stokes equations driven by Wong-Zakai approximations

1.
School of Mathematics and Statistics, Southwest University, Chongqing 400715, China
2.
Department of Mathematics, Brigham Young University, Provo, Utah 84602, USA
3.
Department of Mathematics, New Mexico Institute of Mining and Technology, Socorro, NM 87801, USA

* Corresponding author
* Corresponding author

Received: September 30, 2017

Revised: June 30, 2018

Published: December 2018

The first author is supported by NSF of Chongqing grant cstc2018jcyjA0897

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In this paper, we investigate the asymptotic behavior of the solutions of the two-dimensional stochastic Navier-Stokes equations via the stationary Wong-Zakai approximations given by the Wiener shift. We prove the existence and uniqueness of tempered pullback attractors for the random equations of the Wong-Zakai approximations with a Lipschitz continuous diffusion term. Under certain conditions, we also prove the convergence of solutions and random attractors of the approximate equations when the step size of approximations approaches zero.

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Mathematics Subject Classification: Primary: 35B40, 35B41; Secondary: 37L30.

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