February & March  2004, 11(2&3): 393-411. doi: 10.3934/dcds.2004.11.393

Well-posedness, blowup, and global existence for an integrable shallow water equation

1. 

Department of Mathematics, Zhongshan University, Guangzhou, 510275, China

Received  November 2002 Revised  April 2003 Published  June 2004

We establish the local well-posedness for a recently derived model that combines the linear dispersion of Korteweg-de Veris equation with the nonlinear/nonlocal dispersion of the Camassa-Holm equation, and we prove that the equation has solutions that exist for indefinite times as well as solutions that blow up in finite time. We also derive an explosion criterion for the equation, and we give a sharp estimate of the existence time for solutions with smooth initial data.
Citation: Zhaoyang Yin. Well-posedness, blowup, and global existence for an integrable shallow water equation. Discrete & Continuous Dynamical Systems - A, 2004, 11 (2&3) : 393-411. doi: 10.3934/dcds.2004.11.393
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