Global Bifurcation for Corotating and Counter-Rotating Vortex Pairs

The existence of a local curve corotating and counter-rotating vortex pairs was proven by Hmidi Mateu in via desingularization pair point vortices. In this paper, we construct global continuation these curves. That is, consider solutions which are more than mere perturbation trivial solution. Indeed, while the analysis relies on study linear equation at solution, requires deeper understanding topological properties nonlinear problem. For our proof, adapt powerful analytic bifurcation theorem due to Buffoni Toland, allow for singularity point. both pairs, along either angular fluid velocity vanishes or two patches self-intersect.