Remarks on a multi-dimensional transport equation with nonlocal velocity

Wanwan Zhang

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