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

The long-time behavior 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 non-linear asymptotic L2L2-stability of the conduction solution is obtained.

► Diffusive–convective mixtures in uniformly rotating porous layers, according to the Brinkman law.
► Porous layers are heated from below and salted from above by two salts (most destabilizing case).
► The ultimately boundedness of the solutions (existence of absorbing sets) is shown.
► Necessary and sufficient condition for the global non-linear L2L2-stability of the conduction solution is obtained.