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Local well-posedness in the critical Besov space and persistence properties for a three-component Camassa-Holm system with N-peakon solutions

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  • In this paper we mainly investigate the Cauchy problem of a three-component Camassa-Holm system. By using Littlewood-Paley theory and transport equations theory, we establish the local well-posedness of the system in the critical Besov space. Moreover, we obtain some weighted $L^p$ estimates of strong solutions to the system. By taking suitable weighted functions, we can get the persistence properties of strong solutions on exponential, algebraic and logarithmic decay rates, respectively.
    Mathematics Subject Classification: Primary: 35Q53; Secondary: 35A01, 35B44, 35B65.

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