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

摘要

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 - integral I integral vertical bar x vertical bar <= A vertical bar I vertical bar 1/2 vertical bar u vertical bar(2)Delta(1/vertical bar x vertical bar)dxdt in the localized Morawetz identity to rule out the possibility of energy concentration, instead of the classical Morawetz estimate dependent of the nonlinearity. (c) 2007 Elsevier Inc. All rights reserved.