Consideration in this paper is the generalized fractional Camassa–Holm equation. The local well-posedness is established in Besov space \(B^{s_0}_{2,1}\) with \(s_0=2\nu -\frac{1}{2}\) for \(\nu >\frac{3}{2} \) and \(s_0=\frac{5}{2}\) for \(1<\nu \le \frac{3}{2} \). Then, with a given analytic initial data, the analyticity of the solutions in both variables, globally in space and locally in time, is established. Finally, a blow-up criterion is presented.

中文翻译：

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Besov空间中广义分数阶Camassa-Holm方程的Cauchy问题

本文考虑的是广义分数阶Camassa-Holm方程。在Besov空间\（B ^ {s_0} _ {2,1} \）中以\（s_0 = 2 \ nu-\ frac {1} {2} \）为\（\ nu> \ frac {3} {2} \）和\（s_0 = \ frac {5} {2} \）表示\（1 <\ nu \ le \ frac {3} {2} \）。然后，利用给定的分析初始数据，建立两个变量在全局空间和时间局部的解析性。最后，提出了爆破标准。