Scattering for H^1/2 bounded solutions to the cubic, defocusing NLS in 3 dimensions

Abstract

We show that if a solution of the defocusing cubic NLS in 3d remains bounded in the homogeneous Sobolev norm of order 1/2 in its maximal interval of existence, then the interval is infinite and the solution scatters. No radial assumption is made.

To appear, Tran.Amer.Math.Soc