Finite time blow-up for a multi-dimensional model of the Kiselev-Sarsam equation

Wanwan Zhang

In this paper, we propose and study a multi-dimensional nonlocal active scalar equation of the form \begin{eqnarray*} \partial_tρ+g\mathcal{R}_aρ\cdot \nablaρ= 0,~ρ(\cdot,0)=ρ_{0},…