The dynamics of the focusing NLH with a potential beyond the mass-energy
threshold
The dynamics of the focusing NLH with a potential beyond the mass-energy
threshold
We study the dynamics of the focusing nonlinear Hartree equation with a Kato potential $$ i\partial_t u +\Delta u - Vu = -(|\cdot|^{-\gamma} \ast |u|^2)u, \quad x \in \mathbb{R}^d $$ under some assumptions on the potential $V$. We prove the blow up versus global existence dichotomy for solutions beyond the …