On steady vortex flow in two dimensions, 2

We extend the results of our previous work concerning steady ideal flow with vorticity in a bounded domain to the situation where the domain is unbounded and the flow is uniform at infinity. Prototypical examples include vortex pairs and Foppl vortex wakes behind a cylinder. The existence of solutions and the asymptotic behavior of these solutions in a certain singular limit are established as in part 1 using a direct variational method. The variational principle needed here is rather nonstandard, and so a detailed discussion of its formulation is given. Special difficulties arise for flows in an unbounded domain due to a lack of compactness; consequently, we find that there is nonexistence of solutions in some cases.