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Some properties of the solutions of the N-component Camassa–Holm system with peakons

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Abstract

Considered herein is the Cauchy problem for the N-component Camassa–Holm system with peakons. Owing to the local well-posedness results of the solutions to this problem, we first establish that the solution map is not uniformly continuous in Besov and Hölder spaces through the method of approximate solutions. Next, the Hölder continuity of this solution map in Besov and Sobolev spaces is discussed in detail. Finally, the local Gevrey regularity and analyticity of the solutions are verified by a generalized Ovsyannikov theorem.

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Acknowledgements

The work is supported by Fundamental Research Program of Shanxi Province (Program No. 20210302124259).

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  1. College of Mathematics, Taiyuan University of Technology, Taiyuan, 030024, People’s Republic of China

    Haiquan Wang

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  1. Haiquan Wang
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Wang, H. Some properties of the solutions of the N-component Camassa–Holm system with peakons. Monatsh Math 201, 499–545 (2023). https://doi.org/10.1007/s00605-022-01781-3

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