  We consider divergence-form parabolic equation with measurable uniformly
elliptic matrix and the vector field in a large class containing, in
particular, the vector fields in $L^p$, $p>d$, as well as some vector fields
that are not even in $L_{\rm loc}^{2+\varepsilon}$, $\varepsilon>0$. We
establish H\"{o}lder continuity of the bounded soutions, sharp two-sided
Gaussian bound on the heat kernel, Harnack inequality.
