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

TL;DR

This paper investigates the Gevrey regularity and analyticity of solutions to a weakly dissipative Camassa-Holm system, establishing local and global regularity results and the continuity of the data-to-solution map.

Contribution

It provides the first demonstration of local and global Gevrey regularity and analyticity for this system, along with continuity properties of the solution map.

Findings

Local Gevrey regularity and analyticity established

Global Gevrey regularity in class G_sigma with sigma ≥ 1 proved

Continuity of the data-to-solution map demonstrated

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.