The authors consider the Navier-Stokes equation on a region
only has to satisfy the Poincaré inequality. The weak solutions define a semiprocess depending on an external force
. The authors suppose
is bounded (as a subset of
is the dual of the space of divergence free functions in
) and positive invariant (i.e.
). Under these assumptions they prove the existence of a compact uniform (with respect to
) attractor. In the case of
-dimensional quasi-periodic external force, they also give an upper bound on the Hausdorff dimension of the attractor.