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.

我们考虑时间相关的Landau–Lifshitz–Gilbert方程。我们证明了每个弱解都与（唯一）强解一致，只要后者及时存在。与文献中可获得的结果不同，我们的分析还包括与物理相关的低阶项，例如Zeeman贡献，各向异性，杂散场以及Dzyaloshinskii-Moriya相互作用（这说明了磁性Skyrmions的出现）。此外，我们的证明提供了一个模板，说明了如何将LLG（非线性）耦合到其他（非线性）PDE系统，从而解决更复杂问题的弱强唯一性。