  It has long been known, for the autonomous 2D Navier-Stokes equations with
singular forcing, that there exist unique solutions which gain one derivative,
globally. On the other hand, if the forcing term smooth enough, it is known
that the solution gains two derivatives globally. In this paper, we explore
classical techniques to show that if the force is sufficiently smooth, then the
solution gains two derivatives globally. These methods break down when the
force becomes singular. In this scenario, we use a Littlewood-Paley
decomposition in Fourier space to show that a solutions gain two derivatives
locally in time and the interval of time depends only on the size of the
initial data.
