On the 3D Kelvin-Voigt-Brinkman-Forchheimer equations in some unbounded domains

Considered here is the first initial-boundary value problem for the Kelvin-Voigt-Brinkman-Forchheimer equations in three-dimensional domains satisfying the Poincaré inequality. The existence of a weak solution to the problem is proved by using the Faedo-Galerkin method. Then we show the existence of a unique minimal pullback Dσ-attractor for the process associated to the problem with respect to a large class of non-autonomous forcing terms. Finally, the existence, uniqueness and stability of a stationary solution is studied when the external force is time-independent and “small”.