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On the Cauchy problem for a Camassa-Holm type equation with cubic and quartic nonlinearities

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Abstract

In this paper we first investigate the local well-posedness and global existence with large damping coefficient for the Cauchy problem of a Camassa-Holm type equation with cubic and quartic nonlinearities in nonhomogeneous Besov spaces. Then we obtain a blow-up criteria and present norm inflation which implies ill-posedness for the equation in critical Besov spaces.

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Acknowledgements

This work was partially supported by NNSFC (No. 11671407), FDCT (No. 0091/2018/A3), Guangdong Special Support Program (No. 8-2015), and the key project of NSF of Guangdong province (No. 2016A03031104).

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Authors and Affiliations

  1. Department of Mathematics, Sun Yat-sen University, Guangzhou, 510275, China

    Wenjie Deng & Zhaoyang Yin

  2. Faculty of Information Technology, Macau University of Science and Technology, Macau, China

    Zhaoyang Yin

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  1. Wenjie Deng
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  2. Zhaoyang Yin
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Correspondence to Zhaoyang Yin.

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Communicated by Adrian Constantin.

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Deng, W., Yin, Z. On the Cauchy problem for a Camassa-Holm type equation with cubic and quartic nonlinearities. Monatsh Math 198, 289–310 (2022). https://doi.org/10.1007/s00605-021-01584-y

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