Differential and Integral Equations

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

Vanessa Barros

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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

Permanent link to this document
https://projecteuclid.org/euclid.die/1356012373

Mathematical Reviews number (MathSciNet)
MR2985685

Zentralblatt MATH identifier
1274.35354

Subjects
Primary: 35D05 35E15: Initial value problems 35Q35: PDEs in connection with fluid mechanics

Citation

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


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