The Davey Stewartson system in Weak L^p Spaces

2011/04/07 by Vanessa Barros, Barros, Vanessa
Mathematics · #35D05 #35E15 #35Q35 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35D05 #msc:35E15 #msc:35Q35

paper · pdf · doi:10.48550/arxiv.1104.1454

arxiv created 2011/04/07 · arxiv updated 2011/04/11

Abstract

We study the global Cauchy problem associated to the Davey-Stewartson system in \reⁿ, 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 Schrödinger equation derivated in \citeCVeVi. As a consequence we obtain self-similar solutions.

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