Geodesic
Stability of the Layered Systems at the Presence of the Electric Current
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 9 (2009) no. 1, pp. 24-34 
A. M. Blokhin; R. E. Semenko. Stability of the Layered Systems at the Presence of the Electric Current. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 9 (2009) no. 1, pp. 24-34. http://geodesic.mathdoc.fr/item/VNGU_2009_9_1_a1/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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].

[1] Blokhin A. M., Semenko R. E., “Ob ustoichivosti udarnykh voln v sloistykh strukturakh v prisutstvii elektricheskogo toka”, Vestn. Novosib. gos. un-ta. Ceriya: Matematika, mekhanika, informatika, 8:3 (2008), 26–50 | Zbl

[2] Blokhin A. M., Semenko R. E., “On the Stability of the Shock Waves in Layered Structures at the Presence of the Electric Current”, Quarterly of Applied Mathematics (to appear)

[3] Dorovskii S. V., Dorovskii V. N., “O vozmozhnostyakh elektrorazvedki pri issledovanii ustoichivosti vodoneftyanykh sloistykh sistem”, Geologiya i geofizika, 47:7 (2006), 892–901

[4] Dorovskii S. V., Dorovskii V. N., Blokhin A. M., “O vozmozhnosti metodov elektrorazvedki v issledovanii ustoichivosti vodoneftyanykh sloistykh sistem”, Geologiya i geofizika, 47:11 (2006), 1185–1191

[5] Blokhin A. M., Dorovskii V. N., Problemy matematicheskogo modelirovaniya v teorii mnogoskorostnogo kontinuuma, RAN, Sib. otd-nie, Ob'ed. in-t geologii, geofiziki i mineralogii, In-t matematiki, Novosibirsk, 1994

[6] Gogosov V. V., Polyanskii V. A., “Elektrogidrodinamika: zadacha i prilozheniya, osnovnye uravneniya, razryvnye resheniya”, Itogi nauki i tekhniki. Mekhanika zhidkosti i gaza, 10, 1976, 5–85 | MR | Zbl

[7] Landau L. D., Lifshits E. M., Teoreticheskaya fizika, v. 7, Teoriya uprugosti, Nauka, M., 1987 | MR | Zbl

[8] Kats E. N., Lebedev V. V., Dinamika zhidkikh kristallov, Nauka, M., 1988 | MR

[9] Dorovsky V. N., Dorovsky S. V., “A Hydrodynamic Model of Water-Oil Layered Systems Containing Gas”, Math. Comput. Mod., 35 (2002), 751–757 | DOI | Zbl