  In this paper we prove the existence and uniqueness of weak solutions to the
Dirichlet problem for an elliptic equation with a drift $b$ satisfying
$\operatorname{div} b\le 0$ in $\Omega$. We assume $b$ belongs to some weak
Morrey class which includes in the 3D case, in particular, drifts having a
singularity along the axis $x_3$ with the asymptotic $b(x)\sim c/r$, where
$r=\sqrt{x_1^2+x_2^2}$.
