The inviscid limit for the Landau-Lifshitz-Gilbert equation in the critical Besov space

We prove that in dimensions three and higher the Landau-Lifshitz-Gilbert equation with small initial data in the critical Besov space is globally well-posed in a uniform way with respect to the Gilbert damping parameter. Then we show that the global solution converges to that of the Schr¨odinger map...

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Bibliographic Details
Published in:Science China. Mathematics 2017-11, Vol.60 (11), p.2155-2172
Main Authors: Guo, ZiHua, Huang, ChunYan
Format: Article
Language:English
Subjects:
Applications of Mathematics
Besov空间
Damping
Function space
Landau
Landau-Ginzburg equations
Mathematics
Mathematics and Statistics
Well posed problems
临界
吉尔伯特
方程
极限
粘性
阻尼参数
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Summary:We prove that in dimensions three and higher the Landau-Lifshitz-Gilbert equation with small initial data in the critical Besov space is globally well-posed in a uniform way with respect to the Gilbert damping parameter. Then we show that the global solution converges to that of the Schr¨odinger maps in the natural space as the Gilbert damping term vanishes. The proof is based on some studies on the derivative Ginzburg-Landau equations.
ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-017-9146-x