The dynamics of the focusing NLH with a potential beyond the mass-energy threshold

Shuang Ji, Jing Lu, Fanfei Meng

We study the dynamics of the focusing nonlinear Hartree equation with a Kato potential $$i{\partial }_{t}u+\Delta u-Vu=-(|\cdot {|}^{-\gamma }\ast |u{|}^2)u,x\in {\mathbb{R}}^d$$ under so…