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

Wei  Luo; Zhaoyang Yin

doi:10.3934/dcds.2016019

Article Contents

2016, Volume 36, Issue 9: 5047-5066. Doi: 10.3934/dcds.2016019

This issue Previous Article Global dynamics in a fully parabolic chemotaxis system with logistic source Next Article Correlation integral and determinism for a family of $2^\infty$ maps

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

Wei Luo^1, and
Zhaoyang Yin^2,

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

Received: July 2015

Revised: November 2015

Published: May 2017

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Abstract

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.

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Mathematics Subject Classification: Primary: 35Q53; Secondary: 35A01, 35B44, 35B65.

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