Analysis of Navier-Stokes Models for Flows in Bidisperse Porous Media

Having in view a model proposed by Nield and Kuznetsov (Transp Porous Media 59:325-339, 2005; Transp Porous Media 96:495-499, 2013), we consider a more general system of coupled Navier-Stokes type equations in the incompressible case subject to the homogeneous Dirichlet condition in a bounded domain. We provide a deep theoretical analysis for large classes of equations and coupled systems of Navier-Stokes type with various non-homogeneous terms of reaction type. Existence results are obtained by using a variational approach making use of several fixed point principles and matrix theory.