Strong solutions to the equations of the unconsolidated porous media in 3D thin domains

We prove the existence of global in time strong solutions of incompressible flow equations through isotropic granular (unconsolidated) porous media in thin domains of the form Ωϵ:=R2×(0,ϵ) with ϵ∈(0,1]. Also, we demonstrate that as ϵ→0+ the fluid velocity tends to vanish away from the initial time.