  We characterize the possible behaviors at infinity of weak solutions to the
2D Euler equations in the full plane having bounded velocity and bounded
vorticity. We show that any such solution can be put in the form obtained by
Ph. Serfati in 1995 after a suitable change of reference frame. Our results
build on those of a recent paper of the author's, joint with Ambrose, Lopes
Filho, and Nussenzveig Lopes.
