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On the Cauchy problem for the noncompact Landau-Lifshitz-Gilbert equation. (English) Zbl 1186.35212

Summary: Local well-posedness of the Cauchy problem for the noncompact Landau-Lifshitz-Gilbert equation is investigated via the pseudo-stereographic projection. The 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.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010)
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