具有粗糙初值的Landau-Lifshitz-Gilbert方程的整体解的存在性

Global Existence of Landau-Lifshitz-Gilbert System with Rough Initial Data

关注高维Landau-Lifshitz-Gilbert方程的整体解的存在性问题,证明了当初始值半范数[Z_0(x)]_(BMO(R^n))充分小时,Landau-Lifshitz-Gilbert方程柯西问题存在整体解:通过球面投射的方法,把Landau-Lifshitz-Gilbert方程转化为一个非线性Schr9dinger方程,然后研究该方程的整体解的存在性,最后通过逆运算,得到原Landau-Lifshitz-Gilbert方程的解的整体存在性.

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 Zo（x）∈S^2 with small [ Z0（x） ] BMO（R^n） is established. The method is based on priori estimates of a nonlinear Schrodinger equation obtained from the Landau-Lifshitz-Gilbert equation by the stereographic projection.