Scattering for the focusing ${\dot{H}}^{1/2}$-critical Hartree equation with radial data

Yanfang Gao, Changxing Miao, Guixiang Xu

We investigate the focusing ${\dot{H}}^{1/2}$-critical nonlinear Schrödinger equation (NLS) of Hartree type $i{\partial }_{t}u+\Delta u=-(|\cdot {|}^{-3}\ast |u{|}^2)u$ with ${\dot{H}}^{1/2}$ radi…