Global well-posedness, scattering and blow-up for the energy-critical, focusing Hartree equation in the radial case

Abstract

We establish global existence, scattering for radial solutions to the energy-critical focusing Hartree equation with energy and $\dot{H}^1$ norm less than those of the ground state in $\mathbb{R}\times \mathbb{R}^d$, $d\geq 5$.