On the Cauchy problem for the noncompact Landau–Lifshitz–Gilbert equation

Local well-posedness of the Cauchy problem for the noncompact Landau–Lifshitz–Gilbert equation is investigated via the pseudo-stereographic projection. Existence of global solutions is established for small initial data. In the case of one space dimension global existence theorems are proved for large initial data. © 2008 Elsevier Inc. All rights reserved.