Weak–strong uniqueness for the Landau–Lifshitz–Gilbert equation in micromagnetics. (October 2020)

• Record Type: Journal Article
• Authors: Di Fratta, Giovanni; Innerberger, Michael; Praetorius, Dirk
• Is Part Of: Nonlinear analysis. Volume 55(2020)
• Publication Date: 2020-10
• Subjects: Weak–strong uniqueness -- Landau–Lifshitz–Gilbert equation -- Micromagnetics -- Dzyaloshinskii–Moriya interaction -- Magnetic skyrmions; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2020.103122
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We consider the time-dependent Landau–Lifshitz–Gilbert equation. We prove that each weak solution coincides with the (unique) strong solution, as long as the latter exists in time. Unlike available results in the literature, our analysis also includes the physically relevant lower-order terms like Zeeman contribution, anisotropy, stray field, and the Dzyaloshinskii–Moriya interaction (which accounts for the emergence of magnetic Skyrmions). Moreover, our proof gives a template on how to approach weak–strong uniqueness for even more complicated problems, where LLG is (nonlinearly) coupled to other (nonlinear) PDE systems.