Global Analysis for Rough Solutions to the Davey-Stewartson System

Abstract EN

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.