Self-similar solutions of the Navier-Stokes equations on weak weighted Lorentz spaces

In the present paper, we prove the existence of global solutions for the Navier-Stokes equations in .n when the initial velocity belongs to the weighted weak Lorentz space .n,.(u) with a sufficiently small norm under certain restriction on the weight u. At the same time, self-similar solutions are induced if the initial velocity is, besides, a homogeneous function of degree .1. Also the uniqueness is discussed.