Well-posedness, wave breaking, Holder continuity and periodic peakons for a nonlocal sine-µ-Camassa-Holm equation
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This paper establishes local well-posedness and wave-breaking conditions for a nonlocal sine-type µ-Camassa-Holm equation and presents the Holder continuity of the data-to-solution map and periodic peakon solutions.
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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.
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- europepmc
- last seen: 2026-05-19T01:45:01.086888+00:00
- unpaywall
- last seen: 2026-06-13T06:42:57.164913+00:00