Local well-posedness and blow-up phenomena for a generalized Camassa-Holm equation with peakon solutions

Xi  Tu; Zhaoyang Yin

doi:10.3934/dcds.2016.36.2781

Article Contents

2016, Volume 36, Issue 5: 2781-2801. Doi: 10.3934/dcds.2016.36.2781

This issue Previous Article Random attractor of stochastic Brusselator system with multiplicative noise Next Article Limit cycle bifurcations near generalized homoclinic loop in piecewise smooth differential systems

Local well-posedness and blow-up phenomena for a generalized Camassa-Holm equation with peakon solutions

Xi Tu^1, and
Zhaoyang Yin^2,

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

Received: April 2015

Revised: September 2015

Published: May 2017

Abstract / Introduction Related Papers Cited by

Abstract

In this paper we mainly study the Cauchy problem for a generalized Camassa-Holm equation. First, by using the Littlewood-Paley decomposition and transport equations theory, we establish the local well-posedness for the Cauchy problem of the equation in Besov spaces. Then we give a blow-up criterion for the Cauchy problem of the equation. we present a blow-up result and the exact blow-up rate of strong solutions to the equation by making use of the conservation law and the obtained blow-up criterion. Finally, we verify that the system possesses peakon solutions.

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

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