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

Zhaoyang Yin

doi:10.3934/dcds.2004.11.393

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2004, Volume 11, Issue 2&3: 393-411. Doi: 10.3934/dcds.2004.11.393

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

Zhaoyang Yin^1,

1.
Department of Mathematics, Zhongshan University, Guangzhou, 510275

Received: October 31, 2002

Revised: March 31, 2003

Published: August 2004

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Abstract

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.

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Mathematics Subject Classification: 35G25, 35L05.

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