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March  2017, 37(3): 1575-1601. doi: 10.3934/dcds.2017065

## On an $N$-Component Camassa-Holm equation with peakons

 1 College of Mathematics and Computer Sciences, Yangtze Normal University, Fuling 408100, Chongqing, China 2 Institute of Applied Physics and Computational Mathematics, Beijing 100088, China 3 College of Mathematics and and Statistics, Chongqing University, Chongqing 401331, China

Received  December 2015 Revised  September 2016 Published  December 2016

Fund Project: This work was supported by NSF of China (11401050,11671055,11371384).

In this paper, we are concerned with $N$-Component Camassa-Holm equation with peakons. Firstly, we establish the local well-posedness in a range of the Besov spaces by using Littlewood-Paley decomposition and transport equation theory. Secondly, we present a precise blowup scenario and several blowup results for strong solutions to that system, we then obtain the blowup rate of strong solutions when a blowup occurs. Next, we investigate the persistence property for the strong solutions. Finally, we consider the initial boundary value problem, our approach is based on sharp extension results for functions on the half-line and several symmetry preserving properties of the equations under discussion.

Citation: Yongsheng Mi, Boling Guo, Chunlai Mu. On an $N$-Component Camassa-Holm equation with peakons. Discrete & Continuous Dynamical Systems - A, 2017, 37 (3) : 1575-1601. doi: 10.3934/dcds.2017065
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