Symmetries and skew-symmetries against onset of convection in porous layers salted from above and below

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A triply convective–diffusive fluid mixture saturating a porous horizontal layer in the Darcy–Oberbeck–Boussinesq scheme is studied. The non-linear global stability analysis of the conduction solution – when the layer is heated from below and salted from above and below – is performed. A new methodology based on the introduction of new fields and on looking either for symmetries or for skew-symmetries is applied. In closed form, global asymptotic non-linear stability conditions of the conduction solution, for any value of the salts Prandtl numbers, are found.