Global existence and blow-up of solutions to a nonlocal parabolic equation with singular potential

In this paper, we study a nonlocal parabolic equation with singular potential on a bounded smooth domain with homogeneous Neumann boundary condition. Firstly, we find a threshold of global existence and blow-up to the solutions of the problem when the initial data is at the low energy level, i.e., J(u0)≤d, where J(u0) is the initial energy and d is the mountain-pass level. Moreover, when J(u0)