Longtime behavior of vertical throughflows for binary mixtures in porous layers

Non-linear stability of vertical throughflows in porous layers, uniformly heated and salted from below, is analyzed. The definitively boundedness of the solutions (existence of absorbing sets in the phase space) is proved. Conditions guaranteeing global non-linear asymptotic stability have been found. In closed form, the critical Rayleigh number has been found.

► The definitely boundedness of the solution (existence of absorbing sets) has been obtained.
► “Auxiliary systems” governing the Fourier components of the perturbations are introduced.
► Coincidence between linear stability and global non-linear stability in the L2-norm, is proved.
► Critical value of thermal Rayleigh number for global stability of the throughflow has been found.
► Some numerical values of the critical Rayleigh number, are listed for different throughflows.