Qun Wang, Université Paris Dauphine
602 Pao Yue-Kong Library
The Kirchhoff problem, also known as the N-vortex problem, is a Hamiltonian system that describes interactions of vortices in the plane, and finds application in various phenomena in physics. This system is in general not integrable in Liouville-Arnold sense when the number of vortices is more than 3.
Using the first integral and symmetry consideration, one can overcome the difficulty raised at singularity and existence of critical points of modified action functional will be proved by minimax argument, which corresponds to relative periodic solution of the original Kirchhoff problem.