We prove existence and uniqueness of a weak solution to the incompressible 2D
Euler equations in the exterior of a bounded smooth obstacle when the initial
data is a bounded divergence-free velocity field having bounded scalar curl.
This work completes and extends the ideas outlined by P. Serfati for the same
problem in the whole-plane case. With non-decaying vorticity, the Biot-Savart
integral does not converge, and thus velocity cannot be reconstructed from
vorticity in a straightforward way. The key to circumventing this difficulty is
the use of the Serfati identity, which is based on the Biot-Savart integral,
but holds in more general settings.Comment: 50 page