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• W2014597106 abstract "In this paper we consider the Cauchy problem for the generalized Camassa–Holm equation ut+uQux+∂x(1−∂x2)−1[2ku+Q2+3Q2(Q+1)uQ+1+Q2uQ−1ux2]=0 in Besov space. First, we prove that the solutions to the Cauchy problem for the generalized Camassa–Holm equation do not depend uniformly continuously on the initial data in Hs(R) with s<3/2 when k=0. Second, combining the real interpolations among inhomogeneous Besov spaces with Lemma 5.2.1 of [6] which is called Osgood Lemma (a substitute for Gronwall inequality), we show that the Cauchy problem for the generalized Camassa–Holm equation is locally well-posed in B2,13/2. Finally, we give a blow-up criterion." @default.
• W2014597106 created "2016-06-24" @default.
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• W2014597106 date "2014-04-01" @default.
• W2014597106 modified "2023-10-18" @default.
• W2014597106 title "The Cauchy problem for the generalized Camassa–Holm equation in Besov space" @default.
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• W2014597106 doi "https://doi.org/10.1016/j.jde.2014.01.023" @default.
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