Symmetric three-particle motion in Stokes flow: equilibrium for heavy   spheres in contrast to "end-of-world" for point forces
  A stationary stable solution of the Stokes equations for three identical heavy solid spheres falling in a vertical plane is found. It has no analog in the point-particle approximation. Three spheres aligned horizontally at equal distances evolve towards the equilibrium relative configuration while the point particles collapse onto a single point in a finite time. 
Maria L. Ekiel-Jezewska and Eligiusz Wajnryb