On the Existence of Leapfrogging Pair of Circular Vortex Filaments
arXiv:1803.01507
Abstract
We propose and analyze a system of nonlinear partial differential equations describing the motion of a pair of vortex filaments. Furthermore, for a pair of coaxial circular vortex filaments, we derive a condition for leapfrogging to occur and prove that the condition is necessary and sufficient for the occurrence of leapfrogging.
29 pages, 3 figures