JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2025, Vol. 60 ›› Issue (12): 75-83.doi: 10.6040/j.issn.1671-9352.0.2023.505

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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

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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

CLC Number: 

  • O175
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