Stokes solutions for flow around a sphere and a cylinder with finite decay radius

The classical Stokes solution for creeping flow around a sphere requires an unbounded domain, making it poorly suited for numerical code validation. The present work generalizes this solution by introducing a finite decay radius, yielding closed-form expressions for the velocity field and an explicit formula for the resulting drag force. The solution is exact within a compact spherical domain and recovers the classical Stokes solution in the limit of an infinite decay radius. An analogous generalization is derived for the two-dimensional problem of flow around an infinite cylinder. While the analytical solution diverges for the classical case according to the Stokes paradox, the present approach yields a bounded solution. Both solutions reported here require only simple constant-velocity boundary conditions on a small domain, qualifying them for efficient and unambiguous validation of flow solvers.