Global wellposedness and scattering for 3D Schrödinger equations with harmonic potential and radial data

Abstract

In this paper,we show that spherical bounded energy solution of the defocusing 3D energy critical Schrödinger equation with harmonic potential, $(i{\partial }_t+\frac{\Delta }{2}+\frac{|x{|}^2}{2})u=|u{|}^{4}u$, 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.

39 pages