  The Sadovskii vortex patch is a traveling wave for the two-dimensional
incompressible Euler equations consisting of an odd symmetric pair of vortex
patches touching the symmetry axis. Its existence was first suggested by
numerical computations of Sadovskii in [J. Appl. Math. Mech., 1971], and has
gained significant interest due to its relevance in inviscid limit of planar
flows via Prandtl--Batchelor theory and as the asymptotic state for vortex ring
dynamics. In this work, we prove the existence of a Sadovskii vortex patch, by
solving the energy maximization problem under the exact impulse condition and
an upper bound on the circulation.
