Landau-Lifshitz方程平面波解的全局光滑性

Global Smoothness of the Plane Wave Solutions for Landau-Lifshitz Equation

该文研究了S^(2)上LL方程的n维平面波解.基于Hasimoto变换得到了平面波型的等价薛定谔方程,利用Strichartz估计和傅里叶变换下的能量方法,证明了在小初值条件下该类解的全局存在性.得到的全局解是光滑且空间范数落在任意阶希尔伯特空间中,该文中的结果提高了论文[3]中解的正则性.

In this paper,we study the n-dimensional plane wave solution of the Landau-Lifshtz equation on S^(2).Based on the Hasimoto transformation,the equivalent plane wave type Schrödinger equation is obtained.By the Strichartz estimation and energy method under Fourier transform,the global existence of this solution is proved under a small initial value.The global solution obtained here is smooth and the norm falls in any order Hilbert space.The results in this paper improve the regularity of the solution in the paper[3].