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

Joachim Escher; Olaf Lechtenfeld; Zhaoyang Yin

doi:10.3934/dcds.2007.19.493

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2007, Volume 19, Issue 3: 493-513. Doi: 10.3934/dcds.2007.19.493

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

1.
Institute for Applied Mathematics, Leibniz University of Hanover, D-30167 Hanover
2.
Institute for Theoretical Physics, Leibniz University of Hanover, Appelstraße 2, D-30167 Hanover
3.
Department of Mathematics, Sun Yat-sen University, 510275 Guangzhou

Received: March 31, 2007

Revised: May 31, 2007

Published: August 2007

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Abstract

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.

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Mathematics Subject Classification: 35G25, 35L05.

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

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