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Global existence of Landau-Lifshitz-Gilbert system with rough initial data. (Chinese. English summary) Zbl 1389.35003

Summary: The global solutions to Landau-Lifshitz-Gilbert equation in high dimensions are considered. The global well-posedness of the Cauchy problem of the Landau-Lifshitz-Gilbert equation in \({{\mathbb{R}}^n}\) for any initial data \({Z_0}\left( x \right) \in {S^2}\) with small \({\left[ {{Z_0}\left( x \right)} \right]_{{\text{BMO}}\left( {{{\mathbb{R}}^n}} \right)}}\) is established. The method is based on priori estimates of a nonlinear Schrödinger equation obtained from the Landau-Lifshitz-Gilbert equation by the stereographic projection.

MSC:

35A01 Existence problems for PDEs: global existence, local existence, non-existence
35Q56 Ginzburg-Landau equations
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