2018/03/05 by Aiki, Masashi · 2 citations
#35Q35 (primary) #76B47 (secondary) #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.1803.01507
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.