Existence and uniqueness of weak solutions to the Landau–Lifshitz equation for large ferromagnetic bodies

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 L2$$ {L}^2 $$‐stability of the weak solution.