Global well-posedness and scattering for the mass-critical Hartree equation with radial data

TL;DR

This paper proves global well-posedness and scattering for the mass-critical Hartree equation with radial initial data, extending understanding of solution behavior in the critical setting, especially for large symmetric data.

Contribution

It establishes the first comprehensive results on global solutions and scattering for the mass-critical Hartree equation with large radial data, including the focusing case with mass constraints.

Findings

Global well-posedness for large radial data

Scattering results for solutions in the mass-critical setting

Conditions for focusing case with sub-ground state mass

Abstract

We establish global well-posedness and scattering for solutions to the mass-critical nonlinear Hartree equation $iu_t+\Delta u=\pm(|x|^{-2}*|u|^2)u$ for large spherically symmetric $L^2_x(\Bbb{R}^d)$ initial data; in the focusing case we require, of course, that the mass is strictly less than that of the ground state.