## Differential and Integral Equations

### The Davey Stewartson system in weak $L^p$ spaces

Vanessa Barros

#### Abstract

We study the global Cauchy problem associated to the Davey-Stewartson system in ${\mathbb{R}}^n,\ n=2,3$. Existence and uniqueness of the solution are established 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 derived in [9]. As a consequence we obtain self-similar solutions.

#### Article information

Source
Differential Integral Equations, Volume 25, Number 9/10 (2012), 883-898.

Dates
First available in Project Euclid: 20 December 2012

Barros, Vanessa. The Davey Stewartson system in weak $L^p$ spaces. Differential Integral Equations 25 (2012), no. 9/10, 883--898. https://projecteuclid.org/euclid.die/1356012373