Existence of steady symmetric vortex pairs on a planar domain with an obstacle

We prove an existence theorem for a steady planar flow of an ideal fluid past an obstacle, containing a bounded symmetric vortex pair and approaching a uniform flow at infinity. The vorticity is a rearrangement of a prescribed function. The stream function psi for the flow satisfies the equation -Delta psi = phi o psi in a region bounded by the line of symmetry, where phi is an increasing function that is unknown a priori. The result is obtained from a variational principle in which a functional related. to the kinetic energy is maximised over all flows whose vorticity fields are rearrangements of a prescribed function.