Geodesic
Dynamics of a rotating layer of an ideal electrically conducting incompressible inhomogeneous fluid in an equatorial region
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 11, pp. 1973-1987 
S. I. Peregudin; S. E. Kholodova. Dynamics of a rotating layer of an ideal electrically conducting incompressible inhomogeneous fluid in an equatorial region. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 11, pp. 1973-1987. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_11_a10/
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     title = {Dynamics of a rotating layer of an ideal electrically conducting incompressible inhomogeneous fluid in an equatorial region},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The equations describing the three-dimensional equatorial dynamics of an ideal electrically conducting inhomogeneous rotating fluid are studied. The magnetic and velocity fields are represented as superpositions of unperturbed steady-state fields and those induced by wave motion. As a result, after introducing two auxiliary functions, the equations are reduced to a special scalar one. Based on the study of this equation, the solvability of initial-boundary value problems arising in the theory of waves propagating in a spherical layer of an electrically conducting density-inhomogeneous rotating fluid in an equatorial zone is analyzed. Particular solutions of the scalar equation are constructed that describe small-amplitude wave propagation.

[1] Kholodova S. E., “Volnovye dvizheniya v szhimaemoi stratifitsirovannoi vraschayuscheisya zhidkosti”, Zh. vychisl. matem. i matem. fiz., 47:12 (2007), 2101–2109 | MR

[2] Kholodova S. E., “Dinamika vraschayuschegosya sloya idealnoi elektroprovodnoi neszhimaemoi zhidkosti”, Zh. vychisl. matem. i matem. fiz., 48:5 (2008), 882–898 | MR | Zbl

[3] Kholodova S. E., “Kvazigeostroficheskie dvizheniya vo vraschayuschemsya sloe elektroprovodnoi zhidkosti”, Prikl. mekhan. i tekhn. fiz., 50:1 (2009), 30–41 | MR

[4] Kholodova S. E., “Matematicheskoe modelirovanie krupnomasshtabnykh dvizhenii stratifitsirovannoi elektroprovodnoi zhidkosti v sfericheskom sloe”, Vestn. SPbGU. Ser. 10: Prikl. matem., informatika, protsessy upravleniya, 2009, no. 1, 118–133 | MR

[5] Kholodova S. E., “Volnovye dvizheniya v stratifitsirovannoi elektroprovodnoi vraschayuscheisya zhidkosti”, Zh. vychisl. matem. i matem. fiz., 49:5 (2009), 916–922 | MR | Zbl

[6] Kholodova S. E., Peregudin S. I., Modelirovanie i analiz techenii i voln v zhidkikh i sypuchikh sredakh, Izd-vo SPbGU, SPb., 2009

[7] Alven G., Feltkhammar K.-G., Kosmicheskaya elektrodinamika, Mir, M., 1967

[8] Aleshkov Yu. Z., Matematicheskoe modelirovanie fizicheskikh protsessov, Izd-vo SPbGU, SPb., 2001

[9] Gunko Yu. F., Norin A. V., Filippov B. V., Elektromagnitnaya gazodinamika plazmy, Izd-vo SPbGU, SPb., 2003

[10] Landau L. D., Livshits E. M., Teoreticheskaya fizika, v. VI, Gidrodinamika, Nauka, M., 1988

[11] Landau L. D., Lifshits E. M., Teoreticheskaya fizika, v. VIII, Elektrodinamika sploshnykh sred, Nauka, M., 1992 | MR

[12] Sherklif Dzh., Kurs magnitnoi gidrodinamiki, Mir, M., 1967

[13] Gabov S. A., Sveshnikov A. G., Lineinye zadachi nestatsionarnykh vnutrennikh voln, Nauka, M., 1990

[14] Gabov S. A., Novye zadachi matematicheskoi teorii voln, Nauka, M., 1998 | Zbl

[15] Braginskii S. I., “Magnitogidrodinamika zemnogo yadra”, Geomagnetizm i aeronomiya, 4:5 (1964), 898–916

[16] Braginskii S. I., “Volny v ustoichivo stratifitsirovannom sloe na poverkhnosti zemnogo yadra”, Geomagnetizm i aeronomiya, 3 (1987), 476–482