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• W2901878402 abstract "In this paper, we are concerned with the Cauchy problem of the generalized Camassa–Holm equation. Using a Galerkin-type approximation scheme, it is shown that this equation is well-posed in Sobolev spaces Hs, s>3/2 for both the periodic and the nonperiodic case in the sense of Hadamard. That is, the data-to-solution map is continuous. Furthermore, it is proved that this dependence is sharp by showing that the solution map is not uniformly continuous. The nonuniform dependence is proved using the method of approximate solutions and well-posedness estimates. Moreover, it is shown that the solution map for the generalized Camassa–Holm equation is Hölder continuous in Hr-topology. Finally, with analytic initial data, we show that its solutions are analytic in both variables, globally in space and locally in time." @default.
• W2901878402 created "2018-11-29" @default.
• W2901878402 creator A5001937247 @default.
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• W2901878402 date "2019-05-01" @default.
• W2901878402 modified "2023-10-17" @default.
• W2901878402 title "The Cauchy problem for a generalized Camassa–Holm equation" @default.
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• W2901878402 doi "https://doi.org/10.1016/j.jde.2018.11.019" @default.
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