On the Cauchy Problem of the Camassa-Holm Equation

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.

Keywords

local existence / global existence / Cauchy problem / Camassa-Holm equation / 35Q53 / 76B15

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