  In this paper we give a proof of the existence of global regular solutions to
the Fourier transformed Navier-Stokes system with small initial data in
$\Phi(2)$ via an iteration argument. The proof of the regularity theorem is a
minor modification of the proof given in the paper "Some elementary estimates
for the Navier-Stokes system". So this paper is intended to be just a
complement to the afore mentioned paper.
