On a three-Component Camassa-Holm equation with peakons

Yongsheng Mi; Chunlai Mu

doi:10.3934/krm.2014.7.305

Article Contents

2014, Volume 7, Issue 2: 305-339. Doi: 10.3934/krm.2014.7.305

This issue Previous Article Regularity criteria for the 3D MHD equations via partial derivatives. II Next Article Hypocoercive relaxation to equilibrium for some kinetic models

On a three-Component Camassa-Holm equation with peakons

Yongsheng Mi^1, and
Chunlai Mu^2,

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

Received: March 2013

Revised: January 2014

Published: June 2014

Abstract / Introduction Related Papers Cited by

Abstract

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.

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Mathematics Subject Classification: 35B30, 35G25, 35A10, 35Q53.

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