Abstract This paper mainly discusses the high-order Landau–Lifshitz equation. The author probes both the existence and the uniqueness of global smooth solutions into the Cauchy problem in the Sobolev space by adopting methods of making a priori integral estimation and utilizing continuity.

中文翻译：

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高阶 Landau-Lifshitz 方程的全局适定性

摘要 本文主要讨论高阶Landau-Lifshitz方程。作者采用先验积分估计和利用连续性的方法，探讨了索博列夫空间中柯西问题全局光滑解的存在性和唯一性。