Minimal Energy for the Traveling Waves of the Landau--Lifshitz Equation

André de Laire (1, 2)

1 MEPHYSTO-POST - Méthodes quantitatives pour les modèles aléatoires de la physique
2 LPP - Laboratoire Paul Painlevé - UMR 8524

We consider nontrivial finite energy traveling waves for the Landau--Lifshitz equation with easy-plane anisotropy. Our main result is the existence of a minimal energy for these traveling waves, in dimensions two, three, and four. The proof relies on a priori estimates related to the theory of harmonic maps and the connection of the Landau--Lifshitz equation with the kernels appearing in the Gross--Pitaevskii equation.

Mots clés: and phrases: Landau-Lifshitz equation; Traveling waves; Minimal energy; Harmonic maps; Asymptotic behavior

Domaines: Equations aux dérivées partielles [math.AP]

André de Laire. Minimal Energy for the Traveling Waves of the Landau--Lifshitz Equation. SIAM Journal on Mathematical Analysis, 2014, 46 (1), pp.96-132. ⟨10.1137/130909081⟩. ⟨hal-01951344⟩