Vortex dynamics in the presence of excess energy for the Landau-Lifschitz-Gilbert equation

TL;DR

This paper develops a PDE-based approach to analyze vortex dynamics in the Landau-Lifshitz-Gilbert equation, accommodating instantaneous changes and excess energy without requiring well-prepared initial data.

Contribution

It introduces a novel method for vortex dynamics that handles bubbling events and excess energy, expanding the analytical framework beyond traditional assumptions.

Findings

Provides estimates of the Hodge decomposition of the supercurrent

Analyzes defect measures of weak convergence of stress energy tensor

Addresses Ginzburg-Landau equations with mixed dynamics and excess energy

Abstract

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.