Global well-posedness in Sobolev space implies global existence for weighted \(L^2\) initial data for \(L^2\)-critical NLS (Q2464562)

The authors investigate the relationship between the global well-posedness in Sobolev spaces and the global existence for weighted \(L^2\) initial data for \(L^2\)-critical nonlinear Schrödinger equation. They prove that if global well-posedness holds in Sobolev \(H^s\) space then global existence and scattering holds for initial data in the weighted space with \(\sigma =s\).