The resolution of the Navier-Stokes equations in anisotropic spaces

In this paper we prove global existence and uniqueness for solutions of the 3-dimensional Navier-Stokes equations with small initial data in spaces which are H-delta i in the i-th direction, delta(1)+ delta(2) + delta(3) = 1/2, -1/2 < delta(i) < 1/2 and in a space which is L-2 in the first two directions and B-1,2(1/2) in the third direction, where H and B denote the usual homogeneous Sobolev and Besov spaces.