Ultimately boundedness and stability of triply diffusive mixtures in rotating porous layers under the action of Brinkman law

The long-time behaviour of triply fluid mixtures saturating horizontal porous layers uniformly rotating around the vertical axis, according to the Brinkman law (holding for large pores), is investigated. The most destabilizing case of layers heated from below and salted from above by two salts, is considered. The ultimately boundedness of the solutions (existence of absorbing sets) is shown. A necessary and sufficient condition guaranteeing the global nonlinear asymptotic L^2-stability of the conduction solution, is obtained.