Frontiers of Mathematics in China >

2006 , Vol. 1 >Issue 1: 144 - 159

DOI: https://doi.org/10.1007/s11464-005-0002-6

On the Cauchy Problem of the Camassa–Holm Equation

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  • 1.Department of Mathematics, City University of Hong Kong, Kowloon Tong, Hong Kong, China; 2.Department of Mathematics, The National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Singapore; 3.Department of Mathematics, Nanjing Normal University, Nanjing 210097, China; 4.Department of Mathematics, Yunnan University, Kunming 650091, China

Published date: 05 Mar 2006

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Abstract

The purpose of this paper is to investigate the Cauchy problem of the Camassa Holm equation. By using the abstract method proposed and studied by T. Kato and priori estimates, the existence and uniqueness of the global solution to the Cauchy problem of the Camassa Holm equation in Lp frame under certain conditions are obtained. In addition, the continuous dependence of the solution of this equation on the linear dispersive coefficient contained in the equation is obtained.

Cite this article

DAI Hui-hui, KWEK Keng-Huat, GAO Hong-jun, QU Chao-chun . On the Cauchy Problem of the Camassa–Holm Equation[J]. Frontiers of Mathematics in China, 2006 , 1(1) : 144 -159 . DOI: 10.1007/s11464-005-0002-6

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