Well-posedness and blow-up phenomena for the interacting system of theCamassa-Holm and Degasperis-Procesi equations

Ying Fu; Changzheng Qu; Yichen Ma

doi:10.3934/dcds.2010.27.1025

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2010, Volume 27, Issue 3: 1025-1035. Doi: 10.3934/dcds.2010.27.1025

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Well-posedness and blow-up phenomena for the interacting system of the Camassa-Holm and Degasperis-Procesi equations

1.
Department of Mathematics, Northwest University, Shaanxi 710069
2.
School of Science, Xi’an Jiaotong University, Shaanxi 710049

Received: October 31, 2008

Revised: October 31, 2009

Published: August 2010

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Abstract

In this paper, the well-posedness and blow up phenomena for the interacting system of the Camassa-Holm and Degasperis-Procesi equations are studied. We first establish the local well-posedness of strong solutions for the system. Then the precise blow-up scenarios for the strong solutions to the system are derived.

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Mathematics Subject Classification: Primary: 35B30, 35G25; Secondary: 35L05.

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Well-posedness and blow-up phenomena for the interacting system of the Camassa-Holm and Degasperis-Procesi equations

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