On the Cauchy Problem of the Camassa–Holm Equation

doi:10.1007/s11464-005-0002-6

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Front. Math. China ›› 2006, Vol. 1 ›› Issue (1) : 144-159. DOI: 10.1007/s11464-005-0002-6

On the Cauchy Problem of the Camassa–Holm Equation

DAI Hui-hui¹, KWEK Keng-Huat², GAO Hong-jun³, QU Chao-chun⁴

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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 L^p 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.

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DAI Hui-hui, KWEK Keng-Huat, GAO Hong-jun, QU Chao-chun. On the Cauchy Problem of the Camassa–Holm Equation. Front. Math. China, 2006, 1(1): 144‒159 https://doi.org/10.1007/s11464-005-0002-6