Global Strong Solutions for a One-Dimensional Bilayer Shallow Water Model With a Rigid-Lid Assumption

In this paper, we examine a one-dimensional viscous bilayer shallow water model under the rigid-lid assumption. Each layer is described by the one-dimensional shallow water equations. The work presented in [Discrete and Continuous Dynamical Systems Series B18(1), (2011), 361-383] established the stability of a similar model in the two-dimensional case. The primary focus of this study is to demonstrate the existence of global strong solutions for the proposed model within a periodic domain.