Characterization of minimal-mass blowup solutions to the focusing mass-critical NLS

Abstract

Let d ≤ 4and let u be a global solution to the focusing mass-critical nonlinear Schrödinger equation iut + δm = -|u|4/d-u with spherically symmetric H1/x. initial data and mass equal to that of the ground state Q.We prove that if u does not scatter, then, up to phase rotation and scaling, u is the solitary wave eitQ. Combining this result with that of Merle [Duke Math. J.,69 (1993), pp. 427-453], we obtain that in dimensions d ≤ 4, the only spherically symmetric minimal-mass nonscattering solutions are, up to phase rotation and scaling, the pseudoconformal ground state and the ground state solitary wave. © 2009 Society for Industrial and Applied Mathematics.