On whether zero is in the global attractor of the 2D Navier?Stokes equations

The set of nonzero external forces for which the zero function is in the global attractor of the two-dimensional Navier–Stokes equations is shown to be meagre in a Frechet topology. A criterion in terms of a Taylor expansion in complex time is used to characterize the forces in this set. This leads to several relations between certain Gevrey subclasses of C∞ and a new upper bound for a Gevrey norm of solutions in the attractor, valid in the strip of analyticity in time.