论文标题
BESOV空间中广义的Camassa-Holm方程的不均匀连续性
Non-uniform continuity of the generalized Camassa-Holm equation in Besov spaces
论文作者
论文摘要
在本文中，我们考虑了Hakkaev和Kirchev（2005）\ Cite {Hakkaev 2005}提出的广义Camassa-Holm方程的Cauchy问题。我们证明，在BESOV空间的初始数据上，广义Camassa-Holm方程的解决方案图并不均匀。我们的结果包括目前的工作（2020）\ cite {li 2020，li 2020-1}在Camassa-Holm方程式上，$ Q = 1 $，并扩展了Sobolev Space的先前的不均匀连续性（2015）\ Cite {Mi 2015}到Besov Space。此外，关键空间中的非均匀连续性$ b_ {2，1}^{\ frac {3} {2}}}}}（\ Mathbb {r}）$是我们论文中的第一个考虑。
In this paper, we consider the Cauchy problem for the generalized Camassa-Holm equation proposed by Hakkaev and Kirchev (2005) \cite{Hakkaev 2005}. We prove that the solution map of the generalized Camassa-Holm equation is not uniformly continuous on the initial data in Besov spaces. Our result include the present work (2020) \cite{Li 2020,Li 2020-1} on Camassa-Holm equation with $Q=1$ and extends the previous non-uniform continuity in Sobolev spaces (2015) \cite{Mi 2015} to Besov spaces. In addition, the non-uniform continuity in critical space $B_{2, 1}^{\frac{3}{2}}(\mathbb{R})$ is the first to be considered in our paper.
