Structural stability of the Brinkman–Forchheimer equations for flow in porous media with variable porosity

Petridis, Evangelos [UCL] Papalexandris, Miltiadis [UCL]

In [1] Payne and Straughan established structural stability of the Brinkman–Forchheimer equations for porous media of constant porosity. The main difference with the constant-porosity case, besides the introduction of the porosity as a time-independent field variable, is that the term related to the shear viscous stresses does not reduce to a Laplacian but involves the full deviatoric deformation tensor. Further, there is an additional term due to normal viscous stresses. Herein we establish continuous dependence of solutions with respect to the physical parameters entering the equations, namely, the shear and bulk viscosities and the coefficients of the linear (Darcy) and quadratic (Forchheimer) terms for the interfacial drag. More specifically, we first prove that the shear viscous term is coercive and then establish continuous dependence in the weighted L2 norm, with the porosity being the weight. [1] L. E. Payne, B. Straughan Convergence and Continuous Dependence for the Brinkman–Forchheimer Equations. Stud. Appl. Math. 102 (1999), 419–439.