2D Navier-Stokes equations in Besov spaces of negative order

The Navier-Stokes equation in the bidimensional torus is considered, with initial velocity in the Besov spaces B^(pr)_(-s+2-2/r) and forcing term in L(r) (0, T; B^(pq)_(-s)) for suitable indices s, r, p, q, Results of local existence and uniqueness are proven in the case -1 < -s + 2 - 2/r < 0 and of global existence in the case -1/2 < -s + 2 - 2/r < 0.