Existence and uniqueness of weak solutions to the Landau–Lifshitz equation for large ferromagnetic bodies. (20th November 2022)

• Record Type: Journal Article
• Authors: Xiong, Shengwu; Han, Zeye
• Is Part Of: Mathematical methods in the applied sciences. Volume 46:Number 5(2023)
• Page Start: 5979
• Page End: 5988
• Publication Date: 2022-11-20
• Subjects: Landau–Lifshitz equation -- large ferromagnetic body -- weak solution -- well‐posedness; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.8882
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this paper, we follow the exchange model considered by Han, Tan, and Yang in [SIAM J. Math. Anal., 53(6), 7024–7061 (2021)] to consider the nonexchange case. More precisely, we study the weak solutions of the two‐ or three‐dimensional Landau–Lifshitz equation describing the nonexchange energy model in large ferromagnetic bodies. It is different from the classical Landau–Lifshitz equation because there is no regularization effect of the exchange energy. We prove the existence and uniqueness of global weak solutions. As a by‐product, we obtain the local time L 2 $$ {L}^2 $$ ‐stability of the weak solution.