Global wellposedness and scattering for 3D Schr\"odinger equations with   harmonic potential and radial data
  In this paper,we show that spherical bounded energy solution of the defocusing 3D energy critical Schr\"odinger equation with harmonic potential, $(i\partial_t + \frac {\Delta}2+\frac {|x|^2}2)u=|u|^4u$, exits globally and scatters to free solution in the space $\Sigma=H^1\bigcap\mathcal F H^1$. We preclude the concentration of energy in finite time by combining the energy decay estimates. 
Zhang Xiaoyi