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Continuous dependence on data under the Lipschitz metric for the rotation-Camassa-Holm equation

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Abstract

In this article, we consider the Lipschitz metric of conservative weak solutions for the rotation-Camassa-Holm equation. Based on defining a Finsler-type norm on the tangent space for solutions, we first establish the Lipschitz metric for smooth solutions, then by proving the generic regularity result, we extend this metric to general weak solutions.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Southwest University, Chongqing, 400715, China

    Xinyu Tu

  2. College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, China

    Chunlai Mu & Shuyan Qiu

Authors
  1. Xinyu Tu
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  2. Chunlai Mu
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  3. Shuyan Qiu
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Corresponding author

Correspondence to Xinyu Tu.

Additional information

The first author was supported by Chongqing Post-doctoral Innovative Talent Support Progran, the Fundamental Research Funds for the Central Universities (XDJK2020C054), China Postdoctoral Science Foundation (2020M673102), the Natural Science Foundation of Chongqing, China, (cstc2020jcyj-bshX0071). The second author was supported by the Fundamental Research Funds for the Central Universities (2019CDJCYJ001, 2020CQJQ-Z001), the NSFC (11771062 and 11971082), Chongqing Key Laboratory of Analytic Mathematics and Applications.

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Tu, X., Mu, C. & Qiu, S. Continuous dependence on data under the Lipschitz metric for the rotation-Camassa-Holm equation. Acta Math Sci 41, 1–18 (2021). https://doi.org/10.1007/s10473-021-0101-9

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  • DOI: https://doi.org/10.1007/s10473-021-0101-9

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