Existence of random attractors and the upper semicontinuity for small random perturbations of 2D Navier-Stokes equations with linear damping

Haiyan Li,Bo Wang

doi:10.1515/math-2021-0098

Abstract

Abstract The incompressible 2D stochastic Navier-Stokes equations with linear damping are considered in this paper. Based on some new calculation estimates, we obtain the existence of random attractor and the upper semicontinuity of the random attractors as ε → 0 + \varepsilon \to {0}^{+} on the two-dimensional space.

Highlights

This paper considers the following stochastic Navier-Stokes equations with linear damping in a two-dimensional domain D ⊂ 2
Under the condition f (x) ∈ (L2( 2)), Zhao and Zheng [5] proved the existence of global attractor and studied the deformations of the Navier-Stokes equation by limit behavior
We focus on the random attractor and its upper semicontinuity

Summary

Introduction

This paper considers the following stochastic Navier-Stokes equations with linear damping in a two-dimensional domain D ⊂ 2,. The upper semicontinuity of 2D Navier-Stokes equations 1529 sharp estimates for the fractal dimension of the global attractor. Under the condition f (x) ∈ (L2( 2)), Zhao and Zheng [5] proved the existence of global attractor and studied the deformations of the Navier-Stokes equation by limit behavior. Li [6] established the existence of uniform random attractor for stochastic Navier-Stokes equations in the space H. We derives the existence of random attractors and the upper semicontinuity for small random perturbations of Navier-Stokes equations with linear damping on the twodimensional space, which enriches the theoretical results of the model.

Preliminaries

Existence of random attractors

Upper semicontinuity of attractors