Structural stability for the Forchheimer equations interfacing with a Darcy fluid in a bounded region in $\mathbb{R}^{3}$

Abstract

AbstractThe structural stability for the Forchheimer fluid interfacing with a Darcy fluid in a bounded region in $\mathbb{R}^{3}$ R 3 was studied. We assumed that the nonlinear fluid was governed by the Forchheimer equations in $\Omega _{1}$ Ω 1 , while in $\Omega _{2}$ Ω 2 , we supposed that the flow satisfies the Darcy equations. With the aid of some useful a priori bounds, we were able to demonstrate the continuous dependence results for the Forchheimer coefficient λ.