3 papers
math.AP2025
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},…
math.AP2024
On a multi-dimensional transport equation with nonlocal velocity and fractional dissipation
Wanwan Zhang
This paper aims to investigate a multi-dimensional transport equation with nonlocal velocity and fractional dissipation.The balance between the nonlinearity and dissipation gives r…
math.AP2024
On the blowup of solutions for a nonlocal multi-dimensional transport equation
Wanwan Zhang
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-…