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

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2017,（11）
• 页码范围: 2155-2172
• 页数: 18页
• 语种: 英文
• DOI: 10.1007/s11425-017-9146-x

摘要

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(o)dinger maps in the natural space as the Gilbert damping term vanishes.The proof is based on some studies on the derivative Ginzburg-Landau equations.