ABSTRACT
In this paper we present a rigorous foundation for comparing the long-time dynamics of two Navier-Stokes problems: the first is a 3D problem on a thin domain, and the second is the reduced 2D problem one obtains when the aspect ratio e goes to 0. For this theory we use recent results on the existence of global attractors and inertial forms for both the 2D, and 3D problems. A rigorous comparison of the dynamics residing in certain hyperbolic attractors is made possible by using the new theory of Approximation Dynamics.
