Compressibility

Applied mathematics

Convergence (economics)

Stochastic differential equation

Economics

Statistical physics

Lipschitz continuity

Thermodynamics

Physics

Navier–Stokes equations

Approximations of π

Mathematics

Pullback attractor

Attractor

Mathematical analysis

Uniqueness

Economic growth

Mechanics

Discrete and Continuous Dynamical Systems

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.

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