For generalized landau-lifhsitz equations in multidimensions, zhou yulin and guo doling showed the global existence of weak solution in the case without gilbert term in 1986 关于多维landau-lifshitz方程,1986年周毓麟、郭柏灵就不具gilbert项情形证明了它的整体弱解的存在性。
To investigate the global existence of the smooth solution for landau-lifshitz equation in multidimensions ( n > 2 ), we study the following four topics in this thesis : first, we prove the existence of the solutions of the static landau-lifshitz equation with multi-direct effective field and with dirichlet boundary condition, and establish the stability of the solution of landau-lifshitz equation 为了探索多维(n2)landau-lifshitz方程组的整体光滑解的存在性,我们在这篇论文中研究下列四个课题:第一、我们证明具多向效应场和dirichlet边界条件的landau-lifshitz方程静态解的存在性,并建立landau-lifshitz方程解的稳定性。