By considering a general form of the Landau-Lifshitz equation under the influence of a homogeneous external magnetic fields, we prove that for a ferromagnetic body which occupies a bounded domain Ω in ℝ3 there exists a global weak solution either for the Dirichlet problem or for the Neumann problem. Although there is, in general, non-uniqueness result for the Landau-Lifshitz equation, the uniqueness result for the dynamic equation with constant initial data, which connects with the ground state of the magnetization in physical meanings, is pointed out.
@article{1600,
title = {Global Weak Solutions to the Landau-Lifshitz System in 3D},
journal = {CUBO, A Mathematical Journal},
volume = {8},
year = {2006},
language = {en},
url = {http://dml.mathdoc.fr/item/1600}
}
Fang, Daoyuan; Li, Tailong. Global Weak Solutions to the Landau-Lifshitz System in 3D. CUBO, A Mathematical Journal, Tome 8 (2006) 21 p. http://gdmltest.u-ga.fr/item/1600/