Ground state mass concentration in the L²-critical nonlinear Schrödinger equation below H¹

We consider finite time blowup solutions of the L 2 -critical cubic focusing nonlinear Schrödinger equation on R 2 .Such functions, when in H 1 , are known to concentrate a fixed L 2 -mass (the mass of the ground state) at the point of blowup.Blowup solutions from initial data that is only in L 2 are known to concentrate at least a small amount of mass.In this paper we consider the intermediate case of blowup solutions from initial data in H s , with 1 > s > s Q , whereOur main result is that such solutions, when radially symmetric, concentrate at least the mass of the ground state at the origin at blowup time.