Doubly connected V-states for the planar Euler equations

Abstract

We prove existence of doubly connected V-states for the planar Euler equations which are not annuli. The proof proceeds by bifurcation from annuli at simple "eigenvalues". The bifurcated $V$-states we obtain enjoy a $m$-fold symmetry for some $m\ge 3.$ The existence of doubly connected $V$-states of strict $2$-fold symmetry remains open.

40 pages