Demonstrates that solutions of the generalized Camassa-Holm equation cannot achieve Hölder continuity in Besov spaces, implying limitations on regularity.
In this paper, we prove that the continuity of the solution for the generalized Camassa-Holm equation cannot be improved to the Hölder continuity. To be precise, the solution of the generalized Camassa–Holm equation belongs to \(C([0,T];B^sp,r)\) but not to \(C^α ([0,T];B^sp,r)\) with any \(α ∈ (0,1)\) .
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Qu et al. (2026) studied this question.
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