  We study the global Cauchy problem associated to the Davey-Stewartson system
in $\re^n,\ n=2,3$. Existence and uniqueness of solution are stablished for
small data in some weak $L^p$ space. We apply an interpolation theorem and the
generalization of the Strichartz estimates for the Schr\"odinger equation
derivated in \cite{CVeVi}. As a consequence we obtain self-similar solutions.
