Microstructure-induced finite-speed heat propagation in fluids through porous media: analytical results

In nonisothermal setting microstructural interactions may determine finite speed heat propagation. We consider such an effect in the dynamics of a viscous incompressible complex fluid (that is, one with \textquoteleft active' microstructure) through a porous medium. Nonlocal actions and nonlinear damping are considered as determined by the solid-fluid and microstructural interactions. After a choice of constitutive structures and the introduction of a specific truncation of some higher-order terms, we prove existence and uniqueness of global strong solutions to the balance equations. We also analyze pertinent weak solutions.