Non-autonomous Navier–Stokes Equations and Pullback Attractors

Abstract

In this chapter we study the time asymptotics of solutions to the two-dimensional Navier–Stokes equations. In the first two sections we prove two properties of the equations in a bounded domain, concerning the existence of determining modes and nodes. Then we study the equations in an unbounded domain, in the framework of the theory of infinite dimensional non-autonomous dynamical systems and pullback attractors.