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<p>This paper enhances our understanding of the Landau-Lifshitz-Gilbert (LLG) equation by incorporating the Dzyaloshinskii-Moriya (DM) interaction and V-flow terms. The LLG equation, with the DM term, plays a crucial role in understanding materials with unique magnetic properties, relevant to spintronics and magnetic storage. We employ a comprehensive methodology, including induction, bootstrap arguments, and orthogonal projection methods, to prove the existence and uniqueness of short-time solutions in <i>H</i><sup><i>k</i></sup> spaces. These results contribute to our understanding of the local behavior and enhanced regularity to LLG equation. In addition to theoretical insights, this research provides practical implications, especially regarding the role of DM term in magnetization dynamics, which is crucial for advancing spin-based technologies.</p>

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Very Regular Solution to Landau-Lifshitz-Gilbert Equation with Dzyaloshinskii-Moriya Interaction Term and V-flow Term

  • 期刊论文

  • 发表日期：

    2025年12月12日

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  • Zhen Qiu,
  • Jin-mei Chen,
  • Guang-wu Wang

摘要

This paper enhances our understanding of the Landau-Lifshitz-Gilbert (LLG) equation by incorporating the Dzyaloshinskii-Moriya (DM) interaction and V-flow terms. The LLG equation, with the DM term, plays a crucial role in understanding materials with unique magnetic properties, relevant to spintronics and magnetic storage. We employ a comprehensive methodology, including induction, bootstrap arguments, and orthogonal projection methods, to prove the existence and uniqueness of short-time solutions in Hk spaces. These results contribute to our understanding of the local behavior and enhanced regularity to LLG equation. In addition to theoretical insights, this research provides practical implications, especially regarding the role of DM term in magnetization dynamics, which is crucial for advancing spin-based technologies.