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Local well-posedness and blow-up phenomena for a generalized Camassa-Holm equation with peakon solutions

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  • In this paper we mainly study the Cauchy problem for a generalized Camassa-Holm equation. First, by using the Littlewood-Paley decomposition and transport equations theory, we establish the local well-posedness for the Cauchy problem of the equation in Besov spaces. Then we give a blow-up criterion for the Cauchy problem of the equation. we present a blow-up result and the exact blow-up rate of strong solutions to the equation by making use of the conservation law and the obtained blow-up criterion. Finally, we verify that the system possesses peakon solutions.
    Mathematics Subject Classification: Primary: 35Q53; Secondary: 35A01, 35B44, 35B65.

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