On the stability-instability of vertical throughflows in double diffusive mixtures saturating rotating porous layers with large pores

The long-time behaviour of the solutions of the Darcy–Oberbeck– Boussinesq system modeling fluid motion in horizontal porous layers, is investigated. The layer is supposed to be uniformly heated and salted from below, rotating around the vertical axis, showing large pores. Necessary and sufficient conditions guaranteeing the stability of a vertical constant throughflow are obtained. The non-linear, global, asymptotic $L^2-$ stability of the throughflow solution, is investigated.