Energy-critical Hartree equation with harmonic potential for radial data

In this paper, we consider the defocusing, energy-critical Hartree equation with harmonic potential for the radial data in all dimensions (n >= 5) and show the global well-posedness and scattering theory in the space Sigma = H(1)boolean AND FH(1). We take advantage of some symmetry of the Hartree nonlinearity to exploit the derivative-like properties of the Galilean operators and obtain the energy control as well. Based on Bourgain and Tao's approach, we use a localized Morawetz identity to show the global well-posedness. A key decay estimate comes from the linear part of the energy rather than the nonlinear part, which finally helps us to complete the scattering theory. (C) 2009 Elsevier Ltd. All rights reserved.