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In this paper, we mainly consider the Gevrey regularity and analyticity ofthe solution to a generalized two-component shallow water wave system withhigher-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 provethe global Gevrey regularity and analyticity in time.

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