2017/05/23 by André de Laire, de Laire, André, Philippe Gravejat +1
Computer Science · Engineering · Mathematics · #35A01 #35L05 #35Q55 #35Q60 #37K40 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1705.08146
openalex publication_date 2017/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is well-known that the dynamics of biaxial ferromagnets with a strong\neasy-plane anisotropy is essentially governed by the Sine-Gordon equation. In\nthis paper, we provide a rigorous justification to this observation. More\nprecisely, we show the convergence of the solutions to the Landau-Lifshitz\nequation for biaxial ferromagnets towards the solutions to the Sine-Gordon\nequation in the regime of a strong easy-plane anisotropy. Moreover, we\nestablish the sharpness of our convergence result.\n This result holds for solutions to the Landau-Lifshitz equation in high order\nSobolev spaces. We first provide an alternative proof for local well-posedness\nin this setting by introducing high order energy quantities with better\nsymmetrization properties. We then derive the convergence from the consistency\nof the Landau-Lifshitz equation with the Sine-Gordon equation by using\nwell-tailored energy estimates. As a by-product, we also obtain a further\nderivation of the free wave regime of the Landau-Lifshitz equation.\n