  We study the Stokes problem over convex polyhedral domains on weighted
Sobolev spaces. The weight is assumed to belong to the Muckenhoupt class $A_q$
for $q \in (1,\infty)$. We show that the Stokes problem is well-posed for all
$q$. In addition, we show that the finite element Stokes projection is stable
on weighted spaces. With the aid of these tools, we provide well-posedness and
approximation results to some classes of non-Newtonian fluids.
