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Global Analysis for Rough Solutions to the Davey‐Stewartson System

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  • Han Yang
  • Xiaoming Fan
  • Shihui Zhu

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 Hs with s > 2/5, then there exists a global solution in time, and the Hs 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 Lt,x4 estimate for nonlinear equation with the relatively general defocusing power nonlinearity.

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Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:578701
DOI: 10.1155/2012/578701
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