Global solvability of the Cauchy problem for the Landau-Lifshitz-Gilbert equation in higher dimensions Christof Melcher 35K4535Q6035Q56Landau-Lifshitz-Gilbertcomplex Ginzburg-Landaumoving frames 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. Indiana University Mathematics Journal 2012 text pdf 10.1512/iumj.2012.61.4717 10.1512/iumj.2012.61.4717 en Indiana Univ. Math. J. 61 (2012) 1175 - 1200 state-of-the-art mathematics http://iumj.org/access/