A characterization at infinity of bounded vorticity, bounded velocity solutions to the 2D Euler equations

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.