Large global solutions for nonlinear Schrödinger equations I, mass-subcritical cases

Abstract In this paper, we consider the nonlinear Schrodinger equation, i ∂ t u + Δ u = μ | u | p u , ( t , x ) ∈ R d + 1 , with μ = ± 1 , p > 0 . In this work, we consider the mass-subcritical cases, that is, p ∈ ( 0 , 4 d ) . We prove that under some restrictions on d , p , any radial initial data in the critical space H ˙ s c ( R d ) with compact support, implies global well-posedness.