三维Landau-Lifshitz-Gilbert方程的解的衰减估计

数学物理学报 ›› 2019, Vol. 39 ›› Issue (6): 1443-1455.

三维Landau-Lifshitz-Gilbert方程的解的衰减估计

林俊宇(),万明练(),曹木花()

华南理工大学数学学院广州 510640

收稿日期:2018-07-23 出版日期:2019-12-26 发布日期:2019-12-28
作者简介:林俊宇, E-mail: scjylin@scut.edu.cn|万明练, E-mail: 1841435355@qq.com|曹木花, E-mail: 244901795@qq.com
基金资助:
国家自然科学基金(11571117);广东省自然科学基金(2016A030313451);广州市科技计划项目(201707010040)

Decay Estimates of the Global Solution for the Landau-Lifshitz-Gilbert Equation in Three Dimensions

Junyu Lin(),Minglian Wan(),Muhua Cao()

Department of Mathematics, South China University of Technology, Guangdong 510640

Received:2018-07-23 Online:2019-12-26 Published:2019-12-28
Supported by:
NSFC(11571117);the Natural Science Foundation of Guangdong Province(2016A030313451);the Guangzhou Science and Technology Plan Projects(201707010040)

摘要/Abstract

摘要：

该文关注三维Landau-Lifshitz-Gilbert方程的柯西问题.首先，该文通过能量方法以及连续性办法，得到在适当小的条件下整体光滑解的存在唯一性，并得到解的单调不等式.最后利用该单调不等式以及傅里叶分片法，得到解的衰减估计.

关键词: Landau-Lifshitz-Gilbert方程, 能量估计, 傅里叶分片法

Abstract:

In this paper, the authors consider the Cauchy problem for the Landau-Lifshitz-Gilbert equation in $\mathbb{R}$³. By energy method and standard continuity argument, the authors obtain the global existence and uniqueness of smooth solution under suitable small initial data firstly. After establishing a monotone inequality for this solution, the authors built the time decay rates for this solution by the Fourier splitting method.

Key words: Landau-Lifshitz-Gilbert equation, Energy estimate, Fourier splitting method

中图分类号:

O175.26

林俊宇,万明练,曹木花. 三维Landau-Lifshitz-Gilbert方程的解的衰减估计[J]. 数学物理学报, 2019, 39(6): 1443-1455.

Junyu Lin,Minglian Wan,Muhua Cao. Decay Estimates of the Global Solution for the Landau-Lifshitz-Gilbert Equation in Three Dimensions[J]. Acta mathematica scientia,Series A, 2019, 39(6): 1443-1455.

参考文献 21

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