American Institute of Mathematical Sciences

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September  2007, 19(3): 493-513. doi: 10.3934/dcds.2007.19.493

Well-posedness and blow-up phenomena for the 2-component Camassa-Holm equation

Joachim Escher 1, , Olaf Lechtenfeld 2, and  Zhaoyang Yin 3,

1. 

Institute for Applied Mathematics, Leibniz University of Hanover, D-30167 Hanover, Germany
2. 

Institute for Theoretical Physics, Leibniz University of Hanover, Appelstraße 2, D-30167 Hanover, Germany
3. 

Department of Mathematics, Sun Yat-sen University, 510275 Guangzhou, China

Received  April 2007 Revised  June 2007 Published  July 2007

After some remarks on a possible zero-curvature formulation we first establish local well-posedness for the 2-component Camassa-Holm equation. Then precise blow-up scenarios for strong solutions to the system are derived. Finally we present two blow-up results for strong solutions to the system.
Keywords: blow-up phenomena., strong solutions, local well-posedness, The 2-component Camass-Holm equation.
Mathematics Subject Classification: 35G25, 35L0.
Citation: Joachim Escher, Olaf Lechtenfeld, Zhaoyang Yin. Well-posedness and blow-up phenomena for the 2-component Camassa-Holm equation. Discrete & Continuous Dynamical Systems - A, 2007, 19 (3) : 493-513. doi: 10.3934/dcds.2007.19.493
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