Abstract for Susanna Haziot

Susanna Haziot (Brown University)

Thursday, March 30, 2023

Global bifurcation for corotating vortex pairs

Abstract: The existence of a local curve of corotating vortex pair solutions to the two-dimensional Euler equations was proven by Hmidi and Mateu via a desingularization of a pair of point vortices. In this talk, we construct a global continuation for these local curves. The proof relies on an adaptation of the powerful analytic global bifurcation theorem due to Buffoni and Toland, which allows for the singularity at the bifurcation point. Along the global curve of solutions, either the angular fluid velocity vanishes or the two patches self-intersect. This is a joint work with Claudia Garcia (Universidad Autonoma de Madrid).