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On the Cauchy problem for a weakly dissipative coupled Camassa–Holm system

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Abstract

This paper is concerned with the local well-posedness, wave breaking, blow-up rate and global existence of solutions for a weakly dissipative coupled Camassa–Holm system. First, by using Kato’s theory, we obtain the local well-posedness of solutions in the Sobolev space. We then derive the wave breaking mechanism of solutions, and obtain the blow-up rate of blow-up solutions. Finally, we establish the global existence of solutions.

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Acknowledgements

This work is partially supported by NSFC Grants (Nos. 12225103, 12071065, 11871140 and 12201539) and the National Key Research and Development Program of China (Nos. 2020YFA0713602 and 2020YFC1808301) and Natural Science Foundation of Gansu Province (No. 21JR7RA552) and Natural Science Foundation of Xinjiang Uygur Autonomous Region (No. 2022D01C65).

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Authors and Affiliations

  1. School of Mathematics and Statistics and Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, Changchun, 130024, People’s Republic of China

    Dongxue Zhang, Yonghui Zhou & Shuguan Ji

  2. School of Mathematics and Statistics, Hexi University, Zhangye, 734000, People’s Republic of China

    Yonghui Zhou

  3. College of Mathematics and System Sciences, Xinjiang University, Urumqi, 830046, People’s Republic of China

    Xiaowan Li

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  1. Dongxue Zhang
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  2. Yonghui Zhou
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  3. Shuguan Ji
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  4. Xiaowan Li
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Correspondence to Yonghui Zhou.

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Communicated by Joachim Escher.

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Zhang, D., Zhou, Y., Ji, S. et al. On the Cauchy problem for a weakly dissipative coupled Camassa–Holm system. Monatsh Math 202, 857–873 (2023). https://doi.org/10.1007/s00605-023-01845-y

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