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《山东大学学报(理学版)》 ›› 2025, Vol. 60 ›› Issue (12): 75-83.doi: 10.6040/j.issn.1671-9352.0.2023.505

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Rotation-Camassa-Holm方程和Rotation-μ-Camassa-Holm方程Cauchy解的局部解析性

高亚琴,王海权*,滕凯民   

  1. 太原理工大学数学学院, 山西 太原 030024
  • 发布日期:2025-12-10
  • 通讯作者: 王海权(1991— ),男,讲师,博士,研究方向为偏微分方程. E-mail:hqwangmath@163.com
  • 作者简介:高亚琴(1999— ),女,硕士研究生,研究方向为偏微分方程. E-mail:gaoyaqinmath@163.com*通信作者:王海权(1991— ),男,讲师,博士,研究方向为偏微分方程. E-mail:hqwangmath@163.com
  • 基金资助:
    山西省基础研究计划项目(20210302124259);国家自然科学基金资助项目(12401307)

Local analyticity of the solutions of Cauchy problems of a rotation- μ-Camassa-Holm equation and a rotation-Camassa-Holm equation

GAO Yaqin, WANG Haiquan*, TENG Kaimin   

  1. College of Mathematics, Taiyuan University of Technology, Taiyuan 030024, Shanxi, China
  • Published:2025-12-10

摘要: 利用具有抽象形式的Cauchy-Kovalevsky定理研究一个rotation-μ-Camassa-Holm方程Cauchy问题解的局部解析性,通过推广的Ovsyannikov定理,讨论一个rotation-Camassa-Holm方程Cauchy问题的解在某些Sobolev-Gevrey空间中的局部解析性,并给出解析解存在的时间区间。

关键词: rotation- μ-Camassa-Holm方程, rotation-Camassa-Holm方程, 抽象的Cauchy-Kovalevsky定理, 推广的Ovsyannikov定理, 局部解析性

Abstract: By utilizing the abstact Cauchy-Kovalevsky theorem, this paper first investigates the local analyticity of the solution of Cauchy problem of a rotation- μ-Camassa-Holm equation. Then, the local analyticity of the solution to Cauchy problem associated with a rotation-Camassa-Holm equation in some Sobolev-Gevrey spaces is studied by means of the generalized Ovsyannikov theorem. Besides, the lifespan of the analytic solutions will be given in detail.

Key words: rotation- μ-Camassa-Holm equation, rotation-Camassa-Holm equation, abstract Cauchy-Kovalevsky theorem, generalized Ovsyannikov theorem, local analyticity

中图分类号: 

  • O175
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