Structural stability of the Boussinesq fluid interfacing with a Darcy fluid in a bounded region in [formula omitted

Abstract

The structural stability of the Boussinesq fluid interfacing with a Darcy fluid in a bounded region in R2 was studied. We assumed that the viscous fluid was governed by the Boussinesq equations in Ω1, while in Ω2, we supposed that the flow satisfies the Darcy equations. Some interfacing boundary conditions are imposed. The traditional Poincare´ inequalities can’t be used. With the aid of some useful a priori bounds and some new Poincare´ inequalities, we were able to demonstrate the continuous dependence result on the interface coefficient α. The result showed that the structural stability is valid for the interfacing problem.