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 $\mathbb{R}\times {\mathbb{R}}^d$, $d\ge 5$.

35 pages, 2 figures