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Well-posedness, wave breaking, Holder continuity and periodic peakons for a nonlocal sine-µ-Camassa-Holm equation
  • Guoquan Qin,
  • Zhenya Yan,
  • Boling Guo
Guoquan Qin
Academy of Mathematics and Systems Science Chinese Academy of Sciences

Corresponding Author:[email protected]

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Zhenya Yan
Academy of Mathematics and Systems Science Chinese Academy of Sciences
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Boling Guo
Institute of Applied Physics and Computational Mathematics
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Abstract

In this paper, we investigate the initial value problem of a nonlocal sine-type µ-Camassa-Holm (µCH) equation, which is the µ-version of the sine-type CH equation. We first discuss its local well-posedness in the framework of Besov spaces. Then a sufficient condition on the initial data is provided to ensure the occurance of the wave-breaking phenomenon. We finally prove the H¨older continuity of the data-to-solution map, and find the explicit formula of the global weak periodic peakon solution.