  We give an abstract framework for studying nonautonomous PDEs, called a
generalized evolutionary system. In this setting, we define the notion of a
pullback attractor. Moreover, we show that the pullback attractor, in the weak
sense, must always exist. We then study the structure of these attractors and
the existence of a strong pullback attractor. We then apply our framework to
both autonomous and nonautonomous evolutionary systems as they first appeared
in earlier works by Cheskidov, Foias, and Lu. In this context, we compare the
pullback attractor to both the global attractor (in the autonomous case) and
the uniform attractor (in the nonautonomous case). Finally, we apply our
results to the nonautonomous 3D Navier-Stokes equations on a periodic domain
with a translationally bounded force. We show that the Leray-Hopf weak
solutions form a generalized evolutionary system and must then have a weak
pullback attractor.
