Abstract In this paper, with special choices of a sequence of low frequency and high frequency initial data g n , f n , based on the established existence estimates, by showing that the difference between the solutions initialled with f n + g n and f n will produce a positive lower bound independent of n in a small time, we show that the solution map of a Camassa-Holm-type equation proposed by Novikov is not uniformly continuous on the initial data in Besov spaces B p , r s ( R ) , s > 1 + 1 p , 1 ≤ p , r ≤ ∞ or s = 1 + 1 p , r = 1 , 1 ≤ p ∞ . Our result extends the previous non-uniform continuity in Sobolev spaces (Y. Mi et al., 2019) [29] to Besov spaces.

中文翻译：

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Besov空间中Camassa-Holm型方程初始数据的非均匀连续性

摘要 在本文中，在建立的存在估计的基础上，特别选择了一系列低频和高频初始数据 gn , fn ，通过证明用 fn + gn 和 fn 初始化的解之间的差异将产生一个正的低在短时间内与 n 无关，我们表明 Novikov 提出的 Camassa-Holm 型方程的解图在 Besov 空间 B p , rs ( R ) , s > 1 + 1 中的初始数据上不是一致连续的p , 1 ≤ p , r ≤ ∞ 或 s = 1 + 1 p , r = 1 , 1 ≤ p ∞ 。我们的结果将之前 Sobolev 空间中的非均匀连续性 (Y. Mi et al., 2019) [29] 扩展到 Besov 空间。