  We prove the unique solvability of solutions in Sobolev spaces to the
stationary Stokes system on a bounded Reifenberg flat domain when the
coefficients are partially BMO functions, i.e., locally they are merely
measurable in one direction and have small mean oscillations in the other
directions. Using this result, we establish the unique solvability in
Muckenhoupt type weighted Sobolev spaces for the system with partially BMO
coefficients on a Reifenberg flat domain. We also present weighted a priori
$L_q$-estimates for the system when the domain is the whole Euclidean space or
a half space.
