On the stability of vertical throughflows for binary mixtures in a porous layer

A system modeling fluid motions in horizontal porous layers, uniformly heated from below and salted from above by one salt is analyzed. The definitively boundedness of solutions (existence of absorbing sets in the phase space) is proved. Necessary and sufficient conditions ensuring the linear stability of a constant vertical throughflow have been obtained, via a new approach. Moreover, conditions guaranteeing the global nonlinear asymptotic stability are determined.