The Cauchy problem for the nonstationary Navier-Stokes system is considered in , ,
Here, is the vector of velocity of the liquid, is the pressure.
It is proved that the problem has a unique small regular solution in the homogeneous Besov space and in a homogeneous space which contains the Morrey-type space of measures appeared in Y. Giga and T. Miyakawa [Commun. Partial Differ. Equations 14, 577-618 (1989; Zbl 0681.35072)]. These results imply the existence of small forward self-similar solutions to the Navier-Stokes equations. The uniqueness of solution in is shown, too.