铁磁薄膜中运动 Néel 壁的稳定性
Stability of moving Néel walls in ferromagnetic thin films
AI总结：
本文基于静态 Néel 壁的谱稳定性与一致预解式估计，证明弱外磁场下运动 180 度 Néel 壁的谱稳定、半群衰减及非线性稳定。
摘要：
本文在 Capella、Melcher 和 Otto [5] 提出的面内磁化约化模型下，研究施加足够弱外磁场情形中铁磁薄膜内的运动 180 度 Néel 壁。文中表明，围绕运动 Néel 壁相位的线性化确定了一个谱问题，该问题是围绕静态 Néel 壁线性化的相对有界扰动；静态 Néel 壁是外磁场设为零时的解，并且具有谱稳定性。为证明运动壁的谱稳定性，文中建立了围绕静态壁的线性化算子的一致预解式型估计，并应用线性算子的扰动理论。该谱分析进而构成证明所生成半群的衰减性质，以及在足够弱外磁场情形下运动 Néel 壁在小扰动下非线性稳定性的基础。在姊妹论文 [4] 中建立的静态 Néel 壁稳定性，对获得主要结果起到了关键作用。
英文摘要：
This paper studies moving 180-degree Néel walls in ferromagnetic thin films under the reduced model for the in-plane magnetization proposed by Capella, Melcher and Otto [5], in the case when a sufficiently weak external magnetic field is applied. It is shown that the linearization around the moving Néel wall's phase determines a spectral problem that is a relatively bounded perturbation of the linearization around the static Néel wall, which is the solution when the external magnetic field is set to zero and which is spectrally stable. Uniform resolvent-type estimates for the linearized operator around the static wall are established in order to prove the spectral stability of the moving wall upon application of perturbation theory for linear operators. The spectral analysis is the basis to prove, in turn, both the decaying properties of the generated semigroup and the nonlinear stability of the moving Néel wall under small perturbations, in the case of a sufficiently weak external magnetic field. The stability of the static Néel wall, which was established in a companion paper [4], plays a key role to obtain the main result.
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