Scattering and blow-up dichotomy of the energy-critical nonlinear Schrödinger equation with the inverse-square potential

Abstract: In this paper, we consider the energy critical nonlinear Schr\"odinger equation with a repulsive inverse square potential. In particular, we deal with radial initial data, whose energy is equal to the energy of static solution to the corresponding nonlinear Schr\"odinger equation without a potential. We investigate time behavior of the radial solutions with such initial data.