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In this paper, we show that the Cauchy problem of the 3D nonlinear Schrödinger equation with repulsive potential is globally wellposed if the initial data  u  0  is spherically symmetric and. We also prove that the scattering operator is holomorphic from the radial functions in Σ to themselves. In order to preclude the possible energy concentration, we first show the energy concentration may occur only at finite time by using the decay estimate of potential energy ∥ u ( t )∥ 6 , then we preclude the possible finite time energy concentration by inductive arguments.

Global wellposedness and scattering for 3D energy critical Schrödinger equation with repulsive potential and radial data