On the asymptotics of the negative eigenvalues for an axisymmetric idealmagnetohydrodynamic model
Annales de l'I.H.P. Physique théorique, Tome 48 (1988) no. 1, pp. 39-75.
@article{AIHPA_1988__48_1_39_0,
     author = {Raikov, Georgi},
     title = {On the asymptotics of the negative eigenvalues for an axisymmetric idealmagnetohydrodynamic model},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {39--75},
     publisher = {Gauthier-Villars},
     volume = {48},
     number = {1},
     year = {1988},
     zbl = {0655.76098},
     mrnumber = {947159},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1988__48_1_39_0/}
}
TY  - JOUR
AU  - Raikov, Georgi
TI  - On the asymptotics of the negative eigenvalues for an axisymmetric idealmagnetohydrodynamic model
JO  - Annales de l'I.H.P. Physique théorique
PY  - 1988
DA  - 1988///
SP  - 39
EP  - 75
VL  - 48
IS  - 1
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPA_1988__48_1_39_0/
UR  - https://zbmath.org/?q=an%3A0655.76098
UR  - https://www.ams.org/mathscinet-getitem?mr=947159
LA  - en
ID  - AIHPA_1988__48_1_39_0
ER  - 
Raikov, G. D. On the asymptotics of the negative eigenvalues for an axisymmetric idealmagnetohydrodynamic model. Annales de l'I.H.P. Physique théorique, Tome 48 (1988) no. 1, pp. 39-75. http://www.numdam.org/item/AIHPA_1988__48_1_39_0/

[1] G. Bateman, MHD Instabilities. MIT, Cambridge, Massachusetts, 1978.

[2] C. Mercier, H. Luc, The MHD Approach to the Problem of Plasma Confinement in Closed Magnetic Configurations. EUR 5127e, Luxembourg, 1974.

[3] J.P. Freidberg, Ideal magnetohydrodynamic theory of magnetic fusion systems. Rev. Mod. Phys., t. 54, no. 3, 1982, p. 801-902.

[4] C. Mercier, Un critère nécessaire de stabilité hydrodynamique pour un plasma en symétrie de révolution. Nucl. Fusion, t. 1, 1961, p. 47-53. | MR 154537

[5] J.L. Greene, J.L. Johnson, Interchange instabilities in ideal hydromagnetic theory. Plasma Phys., t. 10, 1968, p. 729-745. | Zbl 0162.59702

[6] D. Lortz, Sufficient stability criteria for general MHD-equilibria. Nucl. Fusion, t. 13, 1973, p. 817-819.

[7] D. Lortz, J. Nührenberg, Comparison between necessary and sufficient criteria for axially symmetric equilibria. Nucl. Fusion, t. 13, 1973, p. 821-827.

[8] J.P. Goedbloed, Spectrum of ideal magnetohydrodynamics of axisymmetric toroidal systems. Phys. Fluids, t. 18, 1975 (10), p. 1258-1268. | MR 398273 | Zbl 0314.76084

[9] J. Descloux, G. Geymonat, On the essential spectrum of an operator relative to the stability of a plasma in a toroidal geometry. École Polytechnique Fédérale de Lausanne Report, October, 1979.

[10] A.E. Lifshits, The continuous spectrum in some problems of mathematical physics. Dokl. Akad. Nauk SSSR, vol. 277, no. 5, 1984, p. 1105-1108 (in Russian). | MR 759975

[11] E., Hamieri, On the essential spectrum of ideal magnetohydrodynamics. Comm. Pure Appl. Math., t. 38, 1985, p. 43-66. | MR 768104 | Zbl 0542.76067

[12] Y.P. Pao, Instabilities in toroidal plasmas. Phys. Fluids, t. 18, 1975 (9), p. 1192-1196.

[13] R.L. Dewar, A.H. Glasser, Ballooning mode spectrum in deneral toroidal systems. Phys. Fluids, t. 26, 1983 (10), p. 3038-3052. | Zbl 0538.76123

[14] G.D. Raikov, Spectral properties of a linear magnetohydrodynamic model with axial symmetry. Vestnik LGU, ser. 4, 1986, vyp. 2, p. 74-76 (in Russian).

[15] M.S. Birman, M.Z. Solomjak, Quantitative analysis in Sobolev imbedding theorems and applications to spectral theory. American Math. Society Translations, Series 2, 114 AMS, Providence, R. I., 1980. | MR 562305 | Zbl 0426.46020

[16] M. Reed, B. Simon, Methods of Modern Mathematical Physics. I, Functional Analysis. Academic Press, New York, 1972. | MR 493419 | Zbl 0242.46001

[17] M. Reed, B. Simon, Methods of Modern Mathematical Physics, IV, Analysis of operators. Academic Press, New York, 1978. | MR 493421 | Zbl 0401.47001

[18] L.D. Landau, E.M. Lifshits, Course of Theoretical Physics, VIII, Electrodynamics of Continuous Media. Pergamon International Library of Science, Technology, Engineering and Social Studies, Pergamon Press, Oxford-Elmsford, N. Y., 1984. | MR 766230

[19] Yu.M. Berezanskii, Expansions in eigenfunctions of self-adjoint operators. Translations of Mathematical Monographs, vol. 17, AMS, Providence, R. I., 1968. | Zbl 0157.16601

[20] O.A. Ladyženskaya, N.N. Uraltseva, Linear and quasilinear equations of elliptic type. Nauka, Moscow, 1964 (in Russian).