The Davey Stewartson system in Weak $L^p$ Spaces

Abstract

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.