Title :

The Cauchy problem for the Landau-Lifshitz-Gilbert equation in BMO and self-similar solutions

Author(s) :

Gutiérrez, Susana [Auteur]
University of Birmingham [Birmingham]
De Laire, André [Auteur]
Méthodes quantitatives pour les modèles aléatoires de la physique [MEPHYSTO-POST]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

NONLINEARITY

Pages :

2522-2563

Publisher :

IOP Publishing

Publication date :

2019

ISSN :

0951-7715

English keyword(s) :

heat-ow for harmonic maps
stability
global well-posedness
Landau-Lifshitz-Gilbert equation
discontinuous initial data
self-similar solutions
dissipative Schrödinger equation
complex Ginzburg-Landau equation
ferromagnetic spin chain

HAL domain(s) :

Mathématiques [math]/Equations aux dérivées partielles [math.AP]
Mathématiques [math]/Physique mathématique [math-ph]

English abstract : [en]

We prove a global well-posedness result for the LandauLifshitz equation with Gilbert damping provided that the BMO semi-norm of the initial data is small. As a consequence, we deduce the existence of self-similar solutions ...
Show more >We prove a global well-posedness result for the LandauLifshitz equation with Gilbert damping provided that the BMO semi-norm of the initial data is small. As a consequence, we deduce the existence of self-similar solutions in any dimension. In the one-dimensional case, we characterize the self-similar solutions associated with an initial data given by some (S^2-valued) step function and establish their stability. We also show the existence of multiple solutions if the damping is strong enough. Our arguments rely on the study of a dissipative quasilinear Schrödinger equation obtained via the stereographic projection and techniques introduced by Koch and Tataru.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL