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

Miao, Changxing; Xu, Guixiang; Zhao, Lifeng

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

Authors

Miao, Changxing

Xu, Guixiang

Zhao, Lifeng

Description

We establish global well-posedness and scattering for solutions to the mass-critical nonlinear Hartree equation $iu_t+Δu=\pm(|x|^{-2}*|u|^2)u$ 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.
38 pages, 1 figure