  We consider the three-dimensional Navier-Stokes equations, with initial data
having second derivatives in the space of pseudomeasures. Solutions of this
system with such data have been shown to exist previously by Cannone and Karch.
As the Navier-Stokes equations are a parabolic system, the solutions gain
regularity at positive times. We demonstrate an improved gain of regularity at
positive times as compared to that demonstrated by Cannone and Karch. We
further demonstrate that the solutions are analytic at all positive times, with
lower bounds given for the radius of analyticity.
