Local well-posedness in the critical Besov space and persistence properties for a three-component Camassa-Holm system with N-peakon solutions
Wei Luo Zhaoyang Yin
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.
keywords: critical Besov space local well-posedness persistence properties. A three-component Camassa-Holm system

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