The Cauchy problem for the Landau-Lifshitz-Gilbert ...
Document type :
Compte-rendu et recension critique d'ouvrage
DOI :
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]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Méthodes quantitatives pour les modèles aléatoires de la physique [MEPHYSTO-POST]
University of Birmingham [Birmingham]
De Laire, André [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Méthodes quantitatives pour les modèles aléatoires de la physique [MEPHYSTO-POST]
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
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]
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 >
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
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