On the stability of vertical constant throughflows for binary mixtures in porous layers

• A system modeling fluid motions in horizontal porous layers, uniformly heated from below and salted from above by one salt, is analyzed.
• The definitely boundedness of solutions (existence of absorbing sets) is proved.
• Via the Rionero approach, necessary and sufficient conditions ensuring the linear stability of a vertical constant throughflow have been obtained.
• Conditions guaranteeing the global non-linear asymptotic stability are determined.

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