Global analysis for rough solutions to the Davey-Stewartson system (Q1938241)

Summary: 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 \(H^s\) with \(s > 2/5\), then there exists a global solution in time, and the \(H^s\) 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 \(L^4_{t,x}\) estimate for nonlinear equation with the relatively general defocusing power nonlinearity.