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

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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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Authors and Affiliations

  1. School of Mathematical Sciences, Institute of Mathematics, Nanjing Normal University, Nanjing, 210023, China

    Lei Mao

  2. School of Mathematical Sciences, Jiangsu Provincial Key Laboratory for NSLSCS, Nanjing Normal University, Nanjing, 210023, China

    Hongjun Gao

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  1. Lei Mao
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Correspondence to Hongjun Gao.

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Communicated by Adrian Constantin.

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Mao, L., Gao, H. The Cauchy problem for generalized fractional Camassa–Holm equation in Besov space. Monatsh Math 195, 451–475 (2021). https://doi.org/10.1007/s00605-021-01513-z

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