2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/144065We 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.SocAnalysis of PDEsAlgebraic Geometry35Q55Scattering for H^1/2 bounded solutions to the cubic, defocusing NLS in 3 dimensionstext