Small oscillations of magnetizable ideal fluid
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 6 (2010), pp. 383-395.

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The small oscillations of a magnetizable ideal fluid in partially filled vessel are considered. Solvability of the initial-boundary problem is proved and the generic properties of the frequencies spectrum of normal free oscillations of fluid are determined. The principle of minimum of the potential energy in the problem on the stability of the fluid equilibrium states is proved.
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I. D. Borisov; T. Yu. Yatsenko. Small oscillations of magnetizable ideal fluid. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 6 (2010), pp. 383-395. http://geodesic.mathdoc.fr/item/JMAG_2010_6_a2/

[1] R. E. Rosensweig, Ferrohydrodynamics, Cambridge Univ. Press, Cambridge, 1985

[2] E. Blums, A. Cebers, M. M. Maiorov, Magnetic Fluids, Walter de Gruyter, Berlin, 1997

[3] I. D. Borisov, “Stability of Equilibrium of a Magnetic Capillary Fluid”, Magnetohydrodynamics, 19:2 (1983), 45–54 | Zbl

[4] H. Kikuraa, T. Sawadaa, T. Tanahashia, L. S. Seob, “Propagation of Surface Waves of Magnetic Fluids in Travelling Magnetic Fields”, J. Magnetism and Magnetic Materials, 85:1–3 (1990), 167–170 | DOI

[5] V. M. Korovin, A. A. Kubasov, “Instability of the Flat Surface of a Magnetic Fluid in a Cylindrical Cavity in the Presence of a Vertical Magnetic Field”, Techn. Phys., 46:1 (1998), 23–30 | MR

[6] V. M. Korovin, “Capillary Instability of the Cylindrical Interface between Ferrofluids in a Magnetic Field with Circular Field Lines”, Techn. Phys., 71:12 (2001), 2–25 | MR

[7] R. Friedrichs, “Pattern and Wave Number Selection in Ferrofluid”, Phys. Rev. E, 64 (2001), 021406, 1–10 | DOI

[8] V. V. Mekhonoshin, A. Lange, “Faraday Instability on Viscous Ferrofluid in a Horizontal Magnetic Feld: Oblique Rolls of Orbitary Orientation”, Phys. Rev. E, 65 (2002), 1–7 | DOI | MR

[9] V. M. Korovin, “Capillary Disintegration of a Configuration Formed by Two Viscous Ferrofluids Surrounding a Current-Carrying Conductor and Having a Cylindrical Interface”, Techn. Phys., 49:12 (2004), 8–15

[10] Ch. Gollwitzer, G. Matthies, R. Richter, I. Rehberg, L. Tobiska, “The Surface Topography of a Magnetic Fluid – a Quantitative Comparison between Experiment and Numerical Simulation”, J. Fluid Mech., 571 (2007), 455–474 | DOI | MR | Zbl

[11] V. M. Korovin, “Capillary Disintegration of a Ferrofluid Cylindrical Film Magnetized to Saturation by an Axial Magnetic Field”, Techn. Phys., 53:5 (2008), 22–28 | DOI | MR

[12] I. D. Borisov, T. Yu. Yatsenko, “On Small Motions of a Magnetizable Viscous Liquid”, Mat. Fiz., Anal., Geom., 10 (2003), 135–146 (Russian) | MR | Zbl

[13] Nikolay D. Kopachevsky, Selim G. Krein, Operator Approach to Linear Problems of Hydrodynamics, Birkhauser Verlang, Basel–Boston–Berlin, 2001 | MR | Zbl

[14] O. A. Ladyzhenskaya, N. N. Ural'tseva, inear and Quasi-Linear Elliptic Equations, 1st ed., Acad. Press, New York–London, 1968 | MR | Zbl

[15] S. M. Nikol'skii, Approximation of Functions of Several Variables and Embedding Theorems, 2nd ed., Revised and Augmented. Nauka, Moscow, 1977 (Russian) | MR

[16] J.-L. Lions, E. Magenes Probèmes aux Limits Non Homogènes et Application, Dunod, Paris, 1968