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The global Gevrey regularity and analyticity of a two-component shallow water system with higher-order inertia operators. (English) Zbl 1416.35206

Summary: 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, \(m = (1 -\partial^2_x)^su\) 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.

MSC:

35Q35 PDEs in connection with fluid mechanics
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35B44 Blow-up in context of PDEs
35C07 Traveling wave solutions
35G25 Initial value problems for nonlinear higher-order PDEs
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
35B65 Smoothness and regularity of solutions to PDEs
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