On the blowup of solutions for a nonlocal multi-dimensional transport equation

In this paper, we revisit the problem of finite-time blowup for a multi-dimensional nonlocal transport equation studied in Dong, Adv. Math. 264 (2014) 747-761. Inspired by a one-dimensional analogous model considered in Li-Rodrigo, Adv. Math. 374 (2020) 1-26, we establish a new weighted nonlinear inequality implying the blow-up by a completely real variable based technique.