Global Gevery regulartiy and analyticity of a weakly dissipative Camassa-Holm equation

Abstract

This work is concerned with the Gevrey regularity and analyticity of the solution to a weakly dissipative Camassa-Holm system. We first demonstrate the local Gevery regularity and analyticity of this equation. Then, we disscuss the continuity of the data-to-solution map. Finally, we obtain the global Gevery regularity of this system in Gevery class $G_{\sigma}$ with $\sigma\geq 1$ in time.