On damped non-linear Choquard equations

This paper studies the damped Schrodinger equation $$\begin{aligned} i\dot{u} +\Delta u+(I_\alpha *|u|^p)|u|^{p-2}u+ia(t)u+ib|u|^{2(q-1)}u+ic\frac{u}{|u|^\beta }+id (-\Delta )^su=0. \end{aligned}$$ Indeed, in the energy sub-critical regime, global well-posedness and scattering versus finite time blow-up of solutions are discussed under some suitable conditions on the damping and the source term.