Parabolic equations with divergence-free drift in space $L_t^l{L}_x^q$

Zhongmin Qian, Guangyu Xi

In this paper we study the fundamental solution $\Gamma (t,x;\tau ,\xi )$ of the parabolic operator $L_t={\partial }_t-\Delta +b(t,x)\cdot \nabla$, where for every $t$, $b(t,\cdot )$ is a dive…