  The Green's functions of Stokes flow are widely used analytical and
computational tools for microscale flows. We adapt a procedure from H.A.
Lorentz for the method of images in Stokes flow to the regularized setting. Our
solutions differ from those previously reported, a surprising result given the
uniqueness theory for elliptic partial differential equations. The discrepancy
originates in the fact that the two version are exact solutions of
inhomogeneous Stokes systems with slightly different forcing on the right-hand
sides. We compare the fluid flows produced by the two methods and conclude that
the Lorentz versions may be advantageous in some settings.
