Global Analysis for Rough Solutions to the Davey-Stewartson System

Han Yang, Xiaoming Fan and Shihui Zhu

Abstract and Applied Analysis, 2012, vol. 2012, 1-22

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.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:578701

DOI: 10.1155/2012/578701

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