The inviscid limit for the Landau-Lifshitz-Gilbert equation in the critical Besov space

TL;DR

This paper establishes the global well-posedness and inviscid limit of the Landau-Lifshitz-Gilbert equation in critical Besov spaces for small initial data in higher dimensions, linking it to Schrödinger maps.

Contribution

It proves the uniform global well-posedness of the Landau-Lifshitz-Gilbert equation and its convergence to Schrödinger maps as damping vanishes, in critical Besov spaces.

Findings

Global well-posedness in higher dimensions for small initial data

Uniform convergence to Schrödinger maps as damping parameter approaches zero

Use of derivative Ginzburg-Landau equations in the proof

Abstract

We prove that in dimensions three and higher the Landau-Lifshitz- Gilbert equation with small initial data in the critical Besov space is globally wellposed in a uniform way with respect to the Gilbert damping parameter. Then we show that the global solution converges to that of the Schrodinger maps in the natural space as the Gilbert damping term vanishes. The proof is based on some studies on the derivative Ginzburg-Landau equations.