On the existence of global strong solutions to 1D bilayer shallow water model

Abstract

. Our study focuses on 1D viscous bilayer shallow water model. The model considered is represented by two superposed immiscible fluids with different physical properties. Each layer is governed by the shallow water equations in one dimension. A regularized model of the considered model has been the subject of some recent studies. Our contribution is to extend the results of the work carried out in [ Nonlinear Analysis, vol (14)2, 1216-1124, (2013) ] by proving the existence of global strong solutions of the considered model.