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

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

2011-04-07

arxiv.org/abs/1104.1454v1

Mathematics

Analysis of PDEs

Scientific paper

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.

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