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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 578701, 22 pages
http://dx.doi.org/10.1155/2012/578701
Research Article

Global Analysis for Rough Solutions to the Davey-Stewartson System

1College of Mathematics, Southwest Jiaotong University, Chengdu 610031, China
2College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, China

Received 7 June 2012; Accepted 15 September 2012

Academic Editor: Abdelghani Bellouquid

Copyright © 2012 Han Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The global well-posedness of rough solutions to the Cauchy problem for the Davey-Stewartson system is obtained. It reads that if the initial data is in with s > 2/5, then there exists a global solution in time, and the norm of the solution obeys polynomial-in-time bounds. The new ingredient in this paper is an interaction Morawetz estimate, which generates a new space-time estimate for nonlinear equation with the relatively general defocusing power nonlinearity.