三维Landau-Lifshitz-Gilbert方程的解的衰减估计

Acta mathematica scientia,Series A ›› 2019, Vol. 39 ›› Issue (6): 1443-1455.

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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)

Abstract

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

CLC Number:

O175.26

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.

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

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