article

Title: Global solvability of the Cauchy problem for the Landau-Lifshitz-Gilbert equation in higher dimensions

Authors: Christof Melcher

Issue: Volume 61 (2012), Issue 3, 1175-1200

Abstract:

$We prove the existence, uniqueness and asymptotics of global smooth solutions for the Landau-Lifshitz-Gilbert equation in dimension $n \ge 3$, valid under a smallness condition of initial gradients in the $L^n$ norm. The argument is based on the method of moving frames that produces a covariant complex Ginzburg-Landau equation and a priori estimates that we obtain by the method of weighted-in-time norms as introduced by Fujita and Kato.$