2012/03/20 by Matthias Kurzke, Kurzke, Matthias, Christof Melcher +5 · 1 citation
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions #math.AP
paper · pdf · doi:10.48550/arxiv.1203.4426
21 pages
arxiv created 2012/03/20 · openalex publication_date 2012/03/20 · arxiv updated 2012/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the Landau-Lifshitz-Gilbert equation for the dynamics of a magnetic vortex system. We present a PDE-based method for proving vortex dynamics that does not rely on strong well-preparedness of the initial data and allows for instantaneous changes in the strength of the gyrovector force due to bubbling events. The main tools are estimates of the Hodge decomposition of the supercurrent and an analysis of the defect measure of weak convergence of the stress energy tensor. Ginzburg-Landau equations with mixed dynamics in the presence of excess energy are also discussed.