# American Institute of Mathematical Sciences

June  2014, 7(2): 305-339. doi: 10.3934/krm.2014.7.305

## On a three-Component Camassa-Holm equation with peakons

 1 College of Mathematics and and Statistics, Chongqing University, Chongqing, 401331, China 2 College of Mathematics and and Statistics, Chongqing University, Chongqing 401331, China

Received  March 2013 Revised  January 2014 Published  March 2014

In this paper, we are concerned with three-Component Camassa-Holm equation with peakons. First, We establish the local well-posedness in a range of the Besov spaces $B^{s}_{p,r},p,r\in [1,\infty],s>\mathrm{ max}\{\frac{3}{2},1+\frac{1}{p}\}$ (which generalize the Sobolev spaces $H^{s}$) by using Littlewood-Paley decomposition and transport equation theory. Second, the local well-posedness in critical case (with $s=\frac{3}{2}, p=2,r=1$) is considered. Then, with analytic initial data, we show that its solutions are analytic in both variables, globally in space and locally in time. 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, Chunlai Mu. On a three-Component Camassa-Holm equation with peakons. Kinetic & Related Models, 2014, 7 (2) : 305-339. doi: 10.3934/krm.2014.7.305
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