@article{AIHPA_1971__15_4_275_0, author = {Maugin, G\'erard A.}, title = {Magnetized deformable media in general relativity}, journal = {Annales de l'institut Henri Poincar\'e. Section A, Physique Th\'eorique}, pages = {275--302}, publisher = {Gauthier-Villars}, volume = {15}, number = {4}, year = {1971}, mrnumber = {290744}, zbl = {0234.73037}, language = {en}, url = {http://www.numdam.org/item/AIHPA_1971__15_4_275_0/} }
TY - JOUR AU - Maugin, Gérard A. TI - Magnetized deformable media in general relativity JO - Annales de l'institut Henri Poincaré. Section A, Physique Théorique PY - 1971 SP - 275 EP - 302 VL - 15 IS - 4 PB - Gauthier-Villars UR - http://www.numdam.org/item/AIHPA_1971__15_4_275_0/ LA - en ID - AIHPA_1971__15_4_275_0 ER -
Maugin, Gérard A. Magnetized deformable media in general relativity. Annales de l'institut Henri Poincaré. Section A, Physique Théorique, Tome 15 (1971) no. 4, pp. 275-302. http://www.numdam.org/item/AIHPA_1971__15_4_275_0/
[1] Physik Zeit., t. 12, 1911, p. 569-575. | JFM
,[2] Ann. Phys. (Leipzig), t. 36, 1911, p. 493. | JFM
,[3] Physik Zeit., t. 12, 1911, p. 854-857. | JFM
,[4] Ann. Phys. (Leipzig), t. 31, 1910, p. 919. | JFM
,[5] Physical Review, t. 95, 1954, p. 1659-1669. | MR | Zbl
and ,[6] Int. J. Engng. Sci., t. 4, 1966, p. 611-670.
and ,[7] Fluid mechanics, Pergamon, Oxford, 1959, chapter XV. | MR
and ,[8] Physical Review, t. 5 , 1940, p. 919.
,[9] Ann. Inst. Henri Poincaré (Paris), t. 10, 1969, p. 67-194. | MR
,[10] Physical Review, t. 94, 1954, p. 1468-1470. | MR
,[11] Théories relativistes de la gravitation et l'électromagnétisme, Masson, édit., Paris, 1955. | Zbl
,[12] Illinois J. of Math., t. 1, 1957, p. 370-388. | MR | Zbl
,[13] Ann. Mat. Pura Appl., t. 38, series 4, 1955, p. 121. | MR | Zbl
,[14] Proceedings of International Symposium, A critical review of the foundations of relativistic and classical thermodynamics, edited by E. B. Stuart, B. Gal-Or and A. J. Brainard, Mono Book, Baltimore, 1970.
, in[15] Arch. Rat. Mech. Anal., t. 1, 1957, p. 54-79; Ann. Inst. Henri Poincaré, t. 2, 1965, p. 151-165. | Numdam | MR | Zbl
,[16] Relativistic hydrodynamics and magnetohydrodynamics, Benjamin, N. Y., 1967. | Zbl
,[17] Théorie relativiste des fluides à spin, Gauthier-Villars, Paris, 1960. | MR
,[18] P. M. M., t. 29, 1965, p. 417; t. 32, 1968, p. 771. Soviet Physics Doklady, t. 10, 1966, n° 9.
,[19] P. M. M., t. 30, 1966, p. 510-530.
,[20] Proc. Royal Soc. London, t. 272 A, 1963, p. 44-53. | Zbl
,[21] Math. Zeitschrift, t. 72, 1959, p. 82-87. | MR | Zbl
,[22] Arch. Rat. Mech. Anal., t. 18, 1965, p. 127-166. | MR | Zbl
,[23] Ann. Mat. Pura Appl., t. 62, 1963, p. 99. | MR | Zbl
,[24] Annalen der Physik, t. 12, 1963, p. 377-395. | MR | Zbl
,[25] J. of Math. Physics, t. 11, 1970, p. 109-113.
,[26] Rend. del Sem. Mat. della Univ. di Padova, t. 34, 1964, p. 1-73. | Numdam | MR | Zbl
,[27]
, Ph. D. Dissertation, Princeton University, Depart. of A. M. S., April 1971.[28] Int. J. Engng. Sci., 1971 (to appear).
and ,[29] Int. J. Engng. Sci., t. 6, 1968, p. 295-307.
,[30] Riv. Mat. Univ. Parma, t. 4, 1964, p. 23-40. | MR | Zbl
,[31] Solid stars », in Scientific American, Feb. 1971, p. 24-31; Journal de Physique, t. 30, suppl. n° 11-12, 1969, p. C3.153-C3.160.
, «[32] Mechanics of continua, J. Wiley, N. Y., 1966. | Zbl
,[33] Arch. Rat. Mech. Anal., t. 39, 1970, p. 89-107. | MR | Zbl
,[34] Int. J. Engng. Sci., t. 2, 1964, p. 59-95. | MR | Zbl
and ,[35] Théorie des distributions, Hermann, Paris, 1966. | MR | Zbl
,[36] Fonctions généralisées et distributions, Masson, édit., Paris, 1964. | MR | Zbl
,[37] Proc. Royal Soc. London, t. A 169, 1939, p. 119. | JFM
,[38] Relativitätstheorie, Vieweg, Braunschweig, vol. 1, 1921, p. 248. | JFM
,[39] The classical theory of fields, Pergamon, Oxford, 1962. | MR | Zbl
and ,[40] General relativity and gravitational waves, Interscience Publ., N. Y., 1961. | MR | Zbl
,[41] R. C. Circ. Mat. Palermo, t. 28, 1909, p. 1; t. 30, 1910, p. 33. | JFM
,[42] Nach. Ges. Wiss. Göttingen, 1908, p. 53; Math. Ann., t. 68, 1910, p. 472. | JFM
,[43] Physica (Holland), t. 37, 1967, p. 284, 297; t. 39, 1968, p. 28, 41, 61, 77, 84.
and ,[44] Communications of the Dublin Institute for advanced studies, sér. A, n° 9, 1953. | Zbl
and ,[45] Proceedings of first symposium of applied math., American Mathematical Soc., N. Y., 1949, p. 148-157. | Zbl
, in[46] Int. J. Engng. Sci., t. 3, 1965, p. 359-377. | MR
and ,[47] For thie term, we need not consider the total variation as was pointed out by Taub, cf. Eq. (4.9) of Ref [12]
[48] (* d *) is the operator of codifferentiation; a star indicating that we take the dual of the quantity at its right, e. g., d *G = dĜ.