On a threeComponent CamassaHolm equation with peakons
Yongsheng Mi  College of Mathematics and and Statistics, Chongqing University, Chongqing, 401331, China (email) Abstract: In this paper, we are concerned with threeComponent CamassaHolm equation with peakons. First, We establish the local wellposedness 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 LittlewoodPaley decomposition and transport equation theory. Second, the local wellposedness 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 halfline and several symmetry preserving properties of the equations under discussion.
Keywords: Besov spaces, CamassaHolm type equation, local wellposedness.
Received: March 2013; Revised: January 2014; Available Online: March 2014. 
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