The Cauchy problem for generalized fractional Camassa–Holm equation in Besov space

Abstract

Consideration in this paper is the generalized fractional Camassa–Holm equation. The local well-posedness is established in Besov space \(B^{s_0}_{2,1}\) with \(s_0=2\nu -\frac{1}{2}\) for \(\nu >\frac{3}{2} \) and \(s_0=\frac{5}{2}\) for \(1<\nu \le \frac{3}{2} \). Then, with a given analytic initial data, the analyticity of the solutions in both variables, globally in space and locally in time, is established. Finally, a blow-up criterion is presented.

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Acknowledgements

The work of Gao is partially supported by the NSFC Grant No. 11531006, and the Jiangsu Center for Collaborative Innovation in Geographical Information Resource and Applications.

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Correspondence to Hongjun Gao.

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Mao, L., Gao, H. The Cauchy problem for generalized fractional Camassa–Holm equation in Besov space. Monatsh Math (2021). https://doi.org/10.1007/s00605-021-01513-z

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Keywords

  • Besov spaces
  • Generalized fractional Camassa–Holm equation
  • Local well-posedness
  • Analyticity
  • Blow-up criterion

Mathematics Subject Classification

  • 35Q53
  • 35B30
  • 35G25