1999/04/28 by S. Gustafson, Stephen J. Gustafson, I. M. Sigal +3
Biochemistry, Genetics and Molecular Biology · Engineering · Mathematics · Physics and Astronomy · #35J60 (Primary) #82D55 (Secondary) #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #Geomagnetism and Paleomagnetism Studies #Mathematical Physics (math-ph) #Navier-Stokes equation solutions #math-ph #math.AP #math.MP #msc:35J60 #msc:82D55
paper · pdf · doi:10.48550/arxiv.math/9904158
28 pages, Latex
arxiv created 1999/04/28 · openalex publication_date 1999/04/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the linearized stability of n-vortex solutions of the magnetic Ginzburg-Landau (or Abelian-Higgs) equations. We prove that the fundamental vortices (n=1,-1) are stable for all values of the coupling constant, k, and we prove that the higher-degree vortices (|n| > 1) are stable for k < 1 and unstable for k > 1. This resolves a long-standing conjecture.