Table of Contents
ISRN Mathematical Analysis
Volume 2013 (2013), Article ID 291823, 29 pages
http://dx.doi.org/10.1155/2013/291823
Review Article

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

Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK

Received 10 March 2013; Accepted 29 April 2013

Academic Editors: I. Fragala, G. Mantica, and A. Peris

Copyright © 2013 James C. Robinson. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.