2016/02/29 by Raghavendra Venkatraman, Venkatraman, Raghavendra
Mathematics · #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #math.AP #math.CA #math.DS
paper · pdf · doi:10.48550/arxiv.1602.09040
36 pages. Final version- exposition was substantially streamlined thanks to a detailed referee report. To appear in Calc. Var. & PDE
arxiv created 2017/04/03 · arxiv updated 2017/04/04
We prove the existence of non-constant time periodic vortex solutions to the Gross-Pitaevskii equations for small but fixed ε > 0. The vortices of these solutions follow periodic orbits to the point vortex system of ordinary differential equations for all time. The construction uses two approaches-- constrained minimization techniques adapted from \citeGS and topological minimax techniques adapted from \citeLinMinMax, applied to a formulation of the problem within a rotational ansatz.