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We prove that the solution map of the two-component Camassa–Holm system is not uniformly continuous as a map from a bounded subset of the Sobolev space Hs(T)×Hr(T) to C([0,1],Hs(T)×Hr(T)) when s?1 and r?0. We also demonstrate the nonuniform continuous property in the continuous function space C1(T)×C1(T). 相似文献
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