Nearly parallel helical vortex filaments in the three-dimensional Euler equations

Klein, Majda, and Damodaran have previously developed a formalized asymptotic motion law describing the evolution of nearly parallel vortex filaments within the framework of the three-dimensional Euler equations for incompressible fluids. In this study, we rigorously justify this model for two configurations: the central configuration consisting of regular polygons of N helical-filaments rotating with constant speed, and the central configurations of N+1 vortex filaments, where an N-polygonal central configuration surrounds a central straight filament.