Attractors and Finite-Dimensional Behaviour in the 2D Navier-Stokes Equations

Abstract

The purpose of this review is to give a broad outline of the dynamical systems approach to the two-dimensional Navier-Stokes equations. This example has led to much of the theory of infinite-dimensional dynamical systems, which is now well developed. A second aim of this review is to highlight a selection of interesting open problems, both in the analysis of the two-dimensional Navier-Stokes equations and in the wider field of infinite-dimensional dynamical systems.