Pullback attractors for nonautonomous 2D Bénard problem in some unbounded domains

In this paper, we study the 2D Benard problem, a system with the Navier–Stokes equations for the velocity field coupled with a convection–diffusion equation for the temperature, in an arbitrary domain (bounded or unbounded) satisfying the Poincare inequality with nonhomogeneous boundary conditions and nonautonomous external force and heat source. The existence of a weak solution to the problem is proved by using the Galerkin method. We then show the existence of a unique minimal finite-dimensional pullback Dσ-attractor for the process associated to the problem. Copyright © 2013 John Wiley & Sons, Ltd.