The irrotational motion generated by two planar stirrers in inviscid fluid

The irrotational motion of an inviscid incompressible fluid driven by two objects, of arbitrary shape, moving at specified velocities in a two-dimensional fluid region is determined. The problem is shown to be equivalent to a standard mathematical problem in potential theory known as the modified Schwarz problem. The solution is given, up to conformal mapping, by the classical Villat formula.