Global well-posedness and scattering for the energy-critical, defocusing Hartree equation for radial data

We consider the defocusing, H˙ 1-critical Hartree equation for the radial data in all dimensions (n 5). We show the global well-posedness and scattering results in the energy space. The new ingredient in this paper is that we first take advantage of the term − I |x| A|I |1/2 |u|2 ( 1 |x|)dx dt in the localized Morawetz identity to rule out the possibility of energy concentration, instead of the classical Morawetz estimate dependent of the nonlinearity. © 2007 Elsevier Inc. All rights reserved