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

TL;DR

This paper proves that radial solutions to the energy-critical focusing Hartree equation in dimensions five and higher are globally well-posed and scatter if their energy and norm are below the ground state.

Contribution

It establishes global existence and scattering results for the energy-critical focusing Hartree equation in the radial case, extending understanding of solution behavior in higher dimensions.

Findings

Global well-posedness for radial solutions below ground state

Scattering results for solutions with energy and norm less than ground state

Applicable in dimensions d ≥ 5

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