Lin, Junyu; Xu, Xiaojie Global existence of Landau-Lifshitz-Gilbert system with rough initial data. (Chinese. English summary) Zbl 1389.35003 J. South China Norm. Univ., Nat. Sci. Ed. 49, No. 3, 97-101 (2017). 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 Keywords:Landau-Lifshitz-Gilbert equation; existence; stereographic projection PDFBibTeX XMLCite \textit{J. Lin} and \textit{X. Xu}, J. South China Norm. Univ., Nat. Sci. Ed. 49, No. 3, 97--101 (2017; Zbl 1389.35003)