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

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.