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

By Vanessa Barros

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

Topics: Mathematics - Analysis of PDEs, 35D05, 35E15, 35Q35
Year: 2011
OAI identifier: oai:arXiv.org:1104.1454
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