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On the Cauchy problem of a new integrable two-component Novikov equation

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Abstract

This paper is devoted to a new integrable two-component Novikov equation with Lax pairs and bi-Hamiltonian structures. Ons the one hand, based on a generalized Ovsyannikov type theorem, we prove the existence and uniqueness of solutions in the Gevrey–Sobolev spaces with the lower bound of the lifespan, and show the continuity of the data-to-solution map. On the other hand, we prove that the strong solutions maintain corresponding properties at infinity within its lifespan provided the initial data decay exponentially and algebraically, respectively.

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Acknowledgements

The work of Mi is partially supported by NSF of China (11671055). The work of Huang is partially supported by NSF of China (11971067,11631008,11771183).

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Authors and Affiliations

  1. College of Mathematics and Statistics, Yangtze Normal University, Chongqing, 408100, People’s Republic of China

    Yongsheng Mi

  2. Institute of Applied Physics and Computational Mathematics, Beijing, 100088, People’s Republic of China

    Daiwen Huang

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  1. Yongsheng Mi
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  2. Daiwen Huang
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Correspondence to Yongsheng Mi.

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Communicated by Adrian Constantin.

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Mi, Y., Huang, D. On the Cauchy problem of a new integrable two-component Novikov equation. Monatsh Math 193, 361–381 (2020). https://doi.org/10.1007/s00605-020-01430-7

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