Motion of a Body Immersed in a Stokes Fluid

In this chapter we study the unsteady motion of a sphere immersed in a Stokes fluid, that is a linear approximation of a fluid governed by the Navier-Stokes equation. The equation of motion for the sphere leads to an integro-differential equation, and we are interested in the asymptotic behavior in time of the solution. We show that the velocity of the sphere slows down in time with an algebraic law, due to the memory effect of the surrounding fluid. We discuss the case of a sphere moving on a straight line, or executing a rotary motion around a fixed axis.