In the paper, we consider the initial value problem to the Camassa-Holm equation in the real-line case. Based on the local well-posedness result and the lifespan, we proved that the data-to-solution map of this problem is not uniformly continuous in nonhomogeneous Besov spaces in the sense of Hadamard. Our obtained result improves considerably the result in \cite{H-K}.

中文翻译：

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Besov 空间中 Camassa-Holm 方程对初始数据的非均匀依赖

在本文中，我们考虑了实线情况下Camassa-Holm方程的初值问题。基于局部适定性结果和寿命，我们证明了该问题的数据到解映射在非齐次 Besov 空间中在 Hadamard 意义上不是一致连续的。我们获得的结果大大改善了 \cite{HK} 中的结果。