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
flow at infinity. The vorticity is a rearrangement of a prescribed function.
The stream function ψ for the flow satisfies the equation
in a region bounded by the line of symmetry, where ϕ is an increasing
is unknown a priori.
The result is obtained from a variational principle in which a functional
the kinetic energy is maximised over all flows whose vorticity fields are
rearrangements of a prescribed function.