Stability of the Layered Systems at the Presence of the Electric Current

In the works [1; 2] the system of hydrodynamical equations for water-oil layered structures with electric current at the presence of the volume charges has been received. Also in this works was discussed a receiving of more simple mathematical model of layered structures in the electrohydrodynamical approximation. The problem of the possible organization of the parametrical instability was discussed in [3; 4].
The main goal of this work is studying of the simple electrohydrodynamical instability in layered structures at the presence of the alternating current with enough small amplitude. This work is a continuation of the works [1; 2].