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      Non-uniform continuity of the generalized Camassa-Holm equation in Besov spaces

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          Abstract

          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.

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          Journal
          03 August 2020
          Article
          2008.00647
          f82f763f-10e7-4066-9938-d1c848d45d21

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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