Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

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

Pages: 493 - 513, Volume 19, Issue 3, November 2007      doi:10.3934/dcds.2007.19.493

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Joachim Escher - Institute for Applied Mathematics, Leibniz University of Hanover, D-30167 Hanover, Germany (email)
Olaf Lechtenfeld - Institute for Theoretical Physics, Leibniz University of Hanover, Appelstra├če 2, D-30167 Hanover, Germany (email)
Zhaoyang Yin - Department of Mathematics, Sun Yat-sen University, 510275 Guangzhou, China (email)

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.

Keywords:  The 2-component Camass-Holm equation, local well-posedness, strong solutions, blow-up phenomena.
Mathematics Subject Classification:  35G25, 35L05.

Received: April 2007;      Revised: June 2007;      Available Online: July 2007.