# Global Gevrey regularity and analyticity of a two-component shallow water system with Higher-order inertia operators

## TL;DR

This paper investigates the Gevrey regularity and analyticity of solutions to a generalized two-component shallow water system with higher-order inertia operators, establishing short-term and global regularity results.

## Contribution

It extends the understanding of regularity properties for shallow water systems with higher-order inertia operators, including global analyticity results.

## Key findings

- Gevrey regularity and analyticity are established for short time.
- Continuity of the data-to-solution map is proved.
- Global in-time Gevrey regularity and analyticity are achieved.

## Abstract

In this paper, we mainly consider the Gevrey regularity and analyticity of the solution to a generalized two-component shallow water wave system with higher-order inertia operators, namely, $m=(1-\partial_x^2)^su$ with $s>1$. Firstly, we obtain the Gevrey regularity and analyticity for a short time. Secondly, we show the continuity of the data-to-solution map. Finally, we prove the global Gevrey regularity and analyticity in time.