Stability for Static Walls in Ferromagnetic Nanowires

The goal of this article is to analyse the time asymptotic stability of one dimensional Bloch wall in ferromagnetic materials. The equation involved in modelling such materials is the Landau-Lifschitz system which is non-linear and parabolic. We demonstrate that the equilibrium states called Bloch walls are asymptotically stable modulo a rotation translation transverse to the wall. The linear part of the perturbed equation admits zero as an eigenvalue forbiding a direct proof