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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 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.

Suggested Citation

  • Han Yang & Xiaoming Fan & Shihui Zhu, 2012. "Global Analysis for Rough Solutions to the Davey-Stewartson System," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-22, November.
    • Handle: RePEc:hin:jnlaaa:578701
    DOI: 10.1155/2012/578701
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