Global existence of Landau-Lifshitz-Gilbert system with rough initial data

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 $R^n$ for any initial data $Z_0\in S^2$ with small $[Z_0]_{BMO(R^n)} is established.$ The method is based on priori estimates of a nonlinear Schr\"odinger equation obtained from the Landau-Lifshitz-Gilbert equation by the stereographic projection.