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The Cauchy Problem for the Camassa-Holm-Novikov Equation

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Abstract

In this paper, we consider the Cauchy problem for the Camassa-Holm-Novikov equation. First, we establish the local well-posedness and the blow-up scenario. Second, infinite propagation speed is obtained as the nontrivial solution u(x, t) does not have compact x-support for any t > 0 in its lifespan, although the corresponding u0(x) is compactly supported. Then, the global existence and large time behavior for the support of the momentum density are considered. Finally, we study the persistence property of the solution in weighted Sobolev spaces.

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Authors and Affiliations

  1. School of Mathematical Sciences, Qufu Normal University, Qufu, 273100, China

    Mingxuan Zhu  (朱铭旋)

  2. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, China

    Zaihong Jiang  (姜在红)

Authors
  1. Mingxuan Zhu  (朱铭旋)
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  2. Zaihong Jiang  (姜在红)
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Corresponding author

Correspondence to Zaihong Jiang  (姜在红).

Additional information

This work was partially supported by the National Natural Science Foundation of China (12071439), the Zhejiang Provincial Natural Science Foundation of China (LY19A010016) and the Natural Science Foundation of Jiangxi Province (20212BAB201016).

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Zhu, M., Jiang, Z. The Cauchy Problem for the Camassa-Holm-Novikov Equation. Acta Math Sci 43, 736–750 (2023). https://doi.org/10.1007/s10473-023-0220-6

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  • DOI: https://doi.org/10.1007/s10473-023-0220-6

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