Well-Posedness and Finite Element Approximation for the Landau-Lifshitz-Gilbert Equation with Spin-Torques
<|reference_start|>Well-Posedness and Finite Element Approximation for the Landau-Lifshitz-Gilbert Equation with Spin-Torques: Spin currents act on ferromagnets by exerting a torque on the magnetisation. This torque is modelled by appending additional terms to the Landau-Lifshitz-Gilbert equation motivating the study of the non-homogeneous Landau-Lifshitz-Gilbert equation. We first prove the existence and uniqueness of high regularity local solutions to this equation using the Faedo-Galerkin method. Then we construct a numerical method for the problem and prove that it converges to a global weak solution of the PDE. Numerical simulations of the problem are also included.<|reference_end|>
@article{vinod2024well-posedness,
    title={Well-Posedness and Finite Element Approximation for the
  Landau-Lifshitz-Gilbert Equation with Spin-Torques},
    author={Noah Vinod and Thanh Tran},
    journal={arXiv preprint arXiv:2407.10429},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.10429},
    primaryClass={math.AP cs.NA math.NA}
}