Global existence of a non-local semilinear parabolic equation with advection and applications to shear flow

Yu Feng, Bingyang Hu, Xiaoqian Xu +1

In this paper, we consider the following non-local semi-linear parabolic equation with advection: for $1\le p<1+\frac{2}{N}$, \begin{equation*} \begin{cases} u_t+v \cdot \nabla u-…