# American Institute of Mathematical Sciences

September  2016, 36(9): 5047-5066. doi: 10.3934/dcds.2016019

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

 1 Department of Mathematics, Sun Yat-sen University, Guangzhou, 510275, China 2 Department of Mathematics, Zhongshan University, Guangzhou, 510275

Received  July 2015 Revised  November 2015 Published  May 2016

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.
Citation: Wei Luo, Zhaoyang Yin. Local well-posedness in the critical Besov space and persistence properties for a three-component Camassa-Holm system with N-peakon solutions. Discrete & Continuous Dynamical Systems, 2016, 36 (9) : 5047-5066. doi: 10.3934/dcds.2016019
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##### References:
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