The Landau–Lifshitz–Bloch Equation in the Thin Film

IF 1.2 3区 数学 Q2 MATHEMATICS, APPLIED Journal of Mathematical Fluid Mechanics Pub Date : 2023-05-30 DOI:10.1007/s00021-023-00801-y
Yuxun He, Huaqiao Wang
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Abstract

In this paper, we study the initial-boundary value problem of the Landau–Lifshitz–Bloch equation in three-dimensional ferromagnetic films, where the effective field contains the stray field controlled by the Maxwell equation, and the exchange field contains exchange constant. Firstly, we establish the existence of weak solutions of the equation by using the Faedo–Galerkin approximation. We also derive its two-dimensional limit equation in a mathematically rigorous way when the film thickness tends towards zero under appropriate compactness conditions. Moreover, we obtain an equation that can better describe the magnetic dynamic behavior of ferromagnetic films with negligible thickness at high temperatures.

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薄膜中的Landau-Lifshitz-Bloch方程
本文研究了三维铁磁薄膜中Landau-Lifshitz-Bloch方程的初边值问题,其中有效场包含由Maxwell方程控制的杂散场,交换场包含交换常数。首先,利用Faedo-Galerkin近似建立了方程弱解的存在性。在适当的致密性条件下,当薄膜厚度趋向于零时,我们也用数学上严格的方法推导了它的二维极限方程。此外,我们还得到了一个方程,可以更好地描述可忽略厚度的铁磁薄膜在高温下的磁动力学行为。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
2.00
自引率
15.40%
发文量
97
审稿时长
>12 weeks
期刊介绍: The Journal of Mathematical Fluid Mechanics (JMFM)is a forum for the publication of high-quality peer-reviewed papers on the mathematical theory of fluid mechanics, with special regards to the Navier-Stokes equations. As an important part of that, the journal encourages papers dealing with mathematical aspects of computational theory, as well as with applications in science and engineering. The journal also publishes in related areas of mathematics that have a direct bearing on the mathematical theory of fluid mechanics. All papers will be characterized by originality and mathematical rigor. For a paper to be accepted, it is not enough that it contains original results. In fact, results should be highly relevant to the mathematical theory of fluid mechanics, and meet a wide readership.
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