  We design and analyze a posteriori error estimators for the Stokes system
with singular sources in suitable $\mathbf{W}^{1,p}\times \mathrm{L}^p$ spaces.
We consider classical low-order inf-sup stable and stabilized finite element
discretizations. We prove, in two and three dimensional Lipschitz, but not
necessarily convex polytopal domains, that the devised error estimators are
reliable and locally efficient. On the basis of the devised error estimators,
we design a simple adaptive strategy that yields optimal experimental rates of
convergence for the numerical examples that we perform.
