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Electrodynamical instability of layered structures. (English) Zbl 1254.35185

Author’s abstract: “We are concerned with a hydrodynamical model of layered structures at the presence of an electric current. We formulate a linearized stability problem for layered structures and prove that the solutions of this problem grow infinitely, which means the destruction of layered structures at the presence of the small-amplitude alternating electric current.”
Accordingly, the authors assemble a thermodynamic model for gassy water-oil layered structures and couple this to reduced Maxwell equations for an applied current. Assuming absence of the gas phase and simple equation of state, they reduce this further to a model of layered dielectrics in electro-hydrodynamical approximation. This is linearized for small-amplitude alternating current in a basic explicit solution and the authors establish unbounded growth for resonant cases.

MSC:

35Q35 PDEs in connection with fluid mechanics
35B35 Stability in context of PDEs
76W05 Magnetohydrodynamics and electrohydrodynamics
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