Landau-Lifshitz方程平面波解的全局光滑性

数学物理学报 ›› 2021, Vol. 41 ›› Issue (3): 729-739.

Landau-Lifshitz方程平面波解的全局光滑性

钟澎洪,陈兴发*()

^{广东第二师范学院数学系广州 510303}

收稿日期:2020-02-21 出版日期:2021-06-26 发布日期:2021-06-09
通讯作者: 陈兴发 E-mail:chenxingfa@gdei.edu.cn
基金资助:
国家自然科学基金青年基金(11601092);广东省青年创新人才项目(2014KQNCX228);广东省科技厅博士启动基金(2014A030310330);广东省特色创新人才项目(2018KTSCX161);广州市科技计划项目(201607010352)

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

Penghong Zhong,Xingfa Chen*()

^{Department of Mathematics, Guangdong University of Education, Guangzhou 510303}

Received:2020-02-21 Online:2021-06-26 Published:2021-06-09
Contact: Xingfa Chen E-mail:chenxingfa@gdei.edu.cn
Supported by:
NSF for Young Scientists of China(11601092);the Project for Young Creative Talents of Ordinary University of Guangdong Province(2014KQNCX228);the PhD Start-up Fund of NSF of Guangdong Province(2014A030310330);the Special Innovation Projects of Universities in Guangdong Province(2018KTSCX161);the Funds of Guangzhou Science and Technology(201607010352)

摘要/Abstract

摘要：

该文研究了$\mathbb{S}^2$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.

关键词: Landau-Lifshitz方程, 存在性, 光滑解, 正则性

Abstract:

In this paper, we study the n-dimensional plane wave solution of the Landau-Lifshtz equation on $\mathbb{S}^2$. 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].

Key words: Landau-Lifshitz equation, Existence, Smooth solution, Regularity

中图分类号:

O175.29

钟澎洪,陈兴发. Landau-Lifshitz方程平面波解的全局光滑性[J]. 数学物理学报, 2021, 41(3): 729-739.

Penghong Zhong,Xingfa Chen. Global Smoothness of the Plane Wave Solutions for Landau-Lifshitz Equation[J]. Acta mathematica scientia,Series A, 2021, 41(3): 729-739.

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