This paper is concerned with the long-time dynamics of some 3D generalized non-autonomous Navier-Stokes equations in a bounded domain governing the motion of fluid flow which comes from a monograph by Ladyzhenskaya. Under some assumptions on the external force and initial data, we prove the existence and structure of uniform attractors for the continuous process.

<p style='text-indent:20px;'>In this paper, we study the asymptotic behavior of the non-autono-mous stochastic 3D Brinkman-Forchheimer equations on unbounded domains. We first define a continuous non-autonomous cocycle for the stochastic equations, and then prove that the existence of tempered random attractors by Ball's idea of energy equations. Furthermore, we obtain that the tempered random attractors are periodic when the deterministic non-autonomous external term is periodic in time.</p>

No abstract

<abstract><p>This paper is concerned with the asymptotic behavior of the stochastic three dimensional Brinkman-Forchheimer equations in some unbounded domains. We first define a continuous random dynamical system for the equations. Then by J. Ball's idea of energy equations, we obtain pullback asymptotic compactness of solutions and prove that the existence of a unique random attractor for the equations.</p></abstract>

We shall show some results for the existence of pullback attractors of 2D Navier-Stokes equation with weak damping, distributed and continuous delay.