Probabilistic well-posedness of the mass-critical NLS with radial data below L2(Rd)

In this paper, we consider the Cauchy problem of the mass-critical nonlinear Schrodinger equation (NLS) with radial data below L2(Rd). We prove almost sure local well-posedness along with small data global existence and scattering. Furthermore, we also derive conditional almost sure global well-posedness of the defocusing NLS under the assumption of a probabilistic a priori energy bound. The main ingredient is to establish the probabilistic radial Strichartz estimates. (C) 2019 Elsevier Inc. All rights reserved.