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 i in the i-th direction, 1 + 2 + 3 = 1 2, 1 2 < i < 1 2 and in a space which is L 2 in the rst two directions and B 1 2 2;1 in the third direction, where H and B denote the usual homogeneous Sobolev and Besov spaces. R esum e Dans cet article on montre l'existence et l'unicit e globale des solutions des