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

Abstract

We consider the defocusing, ${\dot{H}}^1$-critical Hartree equation for the radial data in all dimensions $(n\ge 5)$. 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 $-{\int }_I{\int }_{|x|\le A|I{|}^{1/2}}|u{|}^2\Delta (\frac{1}{|x|})dxdt$ in the localized Morawetz identity to rule out the possibility of energy concentration, instead of the classical Morawetz estimate dependent of the nonlinearity.

arXiv comment23 pages, 1 figure

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