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.
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Crowdy et al. (2007) studied this question.
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