bdim: Biblioteca Digitale Italiana di Matematica

Un progetto SIMAI e UMI

Referenza completa

Georgescu, A. and Palese, L. and Redaelli, A.:
A linear magnetic Bénard problem with tensorial electrical conductivity
Bollettino dell'Unione Matematica Italiana Serie 8 9-B (2006), fasc. n.1, p. 197-214, (English)
pdf (390 Kb), djvu (171 Kb). | MR 2204907 | Zbl 1150.76034

Sunto

Si studia, nell'ipotesi che sussista il principio di scambio delle stabilità, il problema agli autovalori che governa la stabilità lineare della quiete per un problema di Benard elettroanisotropo, in presenza di correnti di Hall e di ion-slip. Si risolvono due problemi agli autovalori dello stesso ordine derivanti dall'aver scomposto le perturbazioni nelle loro parti pari e dispari, espresse come somme di serie di Fourier di opportuni insiemi totali in spazi di Hilbert separabili. Si determinano le curve neutrali applicando il metodo di Budiansky-DiPrima Si prova l'effetto instabilizzante delle correnti elettroanisotrope.
Referenze Bibliografiche
[1] KAMLA ABANI - K.M. SRIVASTAVA, Rayleigh-Taylor instability of a viscous plasma inthe Presence of Hall current, Il Nuovo Cimento, 26, 2 (1975), 419-432.
[2] S. CHANDRASEKHAR, Hydrodynamic and hydromagnetic stability, Clarendon, Oxford, 1968. | MR 128226
[3] R. C. DI PRIMA, Some variational principles for problems in hydrodynamic and hydromagnetic stability, Quart. Appl. Math., 18, 4 (1961), 375-385. | fulltext (doi) | MR 116767
[4] D. EBEL - M.C. SHEN, On the linear stability of a toroidal plasma with resistivity, viscosity and Hall current, J. Math.Anal. Appl., 125 (1987), 81-103. | fulltext (doi) | MR 891351 | Zbl 0649.76023
[5] D. EBEL - M. M. SHEN, Linearization principle for a toroidal Hall current plasma with viscosity and resistivity, Annali Mat. Pura Appl., 150 (1988), 39-65. | fulltext (doi) | MR 946029 | Zbl 0666.76153
[6] A. GEORGESCU, Hydrodynamic stability theory, Kluwer, Dordrecht, 1985. | fulltext (doi) | MR 850008 | Zbl 0608.76035
[7] A. GEORGESCU, Variational formulation of some nonselfadjoint problems occurring in Benard instability theory, I, Series in Mathematics 35/1977 INCREST, Bucharest.
[8]A. GEORGESCU - L. PALESE - D. PASCA - M. BUICAN, Critical hydromagnetic stability of a thermodiffusive state, Rev. Roumaine Math. Pures et Appl., 38, 10 (1993), 831840. | MR 1264602
[9]A. GEORGESCU - L. PALESE, Neutral stability hypersurfaces for an anisotropic M.H.D. thermodiffusive mixture. III. Detection of false secular manifolds among the bifurcation characteristic manifolds, Rev. Roumaine Math. Pures et Appl., 41, 12 (1996), 35-49. | MR 1404641 | Zbl 0857.76032
[10]J. S. GRADSHTEYN - I. M. RYZHIK, Table of integrals, series, and products, Academic, New York, 1980. | MR 669666 | Zbl 0521.33001
[11]D. D. JOSEPH, Stability of fluid motions, vols. I, II, Springer, Berlin, 1976. | MR 627612
[12]M. MAIELLARO - L. PALESE, Sui moti M.H.D. stazionari di una miscela binaria in uno strato obliquo poroso in presenza di effetto Hall e sulla loro stabilita, Rend. Accad. Sc. Mat. Fis., Napoli, IV, XLVI (1979), 471-481. | Zbl 0441.76041
[13]M. MAIELLARO - L. PALESE, Electrical anisotropic effects on thermal instability. Int. J. Engng. Sc., 22, 4 (1984), 411-418. | Zbl 0534.76045
[14]M. MAIELLARO - L. PALESE - A. LABIANCA, Instabilizing-stabilizing effects of M.H.D. anisotropic currents, Int. J. Engng. Sc., 27, 11 (1989), 1353-1359. | fulltext (doi) | MR 998286 | Zbl 0693.76059
[15]M. MAIELLARO - A. LABIANCA, On the non linear stability in anisotropic MHD with applications to Couette Poiseuille flows. Int. J. Engng. Sc., 40, (2002), 1053-1068. | Zbl 1211.76153
[16]S. G. MIKHLIN, Mathematical physics, an advanced course, North Holland, Amsterdam, 1970. | MR 286325 | Zbl 0202.36901
[17]G. MULONE - S. RIONERO, On the non linear stability of the rotating Benard problemvia the Lyapunov direct method, J. Math.Anal. Appl., 144 (1989), 109-127. | fulltext (doi) | MR 1022564 | Zbl 0682.76037
[18]G. MULONE - S. RIONERO, On the stability of the rotating Benard problem, Bull. Tech.Univ. Istanbul, 47 (1994), 181-202. | MR 1321950 | Zbl 0864.76030
[19]G. MULONE - F. SALEMI, Some continuous dependence theorems in M.H.D. with Hall and ion-slip currents in unbounded domains, Rend. Accad. Sci. Fis. Mat. Napoli, IV, 55 (1988), 139-152. | MR 1136744 | Zbl 1145.76473
[20]SH. I. PAI, Magnetohydrodynamics and plasma dynamics, Springer, Berlin, 1962.
[21]L. PALESE, Sull'instabilita gravitazionale e sulla propagazione ondosa per un fluido elettroconduttore anisotropo inquinato, Atti Sem. Mat. Fis. Univ. Modena,XLII (1994), 1-17.
[22]L. PALESE, Electroanisotropic effects on the thermal instability of an anisotropic binary fluid mixture, J. of Magnetohydrodynamics and Plasma Research, 7, 2/3 (1997), 101-120.
[23]L. PALESE - A. GEORGESCU - D. PASCA, Stability of a binary mixture in a porous medium with Hall ion-slip effect and Soret Dufour currents, Analele Univ. Oradea, 3 (1993), 92-96.
[24] L. PALESE - A. Georgescu, A linear magnetic Benard problem with Hall effect. Application of Budiansky-DiPrima method, Rapporti Int. Dip. Mat. Bari, 15 (2003).
[25]L. PALESE - A. GEORGESCU - D. PASCA - D. BONEA, Thermosolutal instability of a compressible Soret-Dufour mixture with Hall and ion-slip currents through a porous medium, Rev. Roumaine Mec. Appl., 42, 3-4, (1997) 279 -296. | MR 2165211
[26]S. RIONERO - G. MULONE, A non linear stability analysis of the magnetic Benard problem through the Lyapunov direct method, Arch. Rational Mech. Anal., 103 (1988), 347-368. | fulltext (doi) | MR 955532 | Zbl 0666.76068
[27] R. C. SHARMA - K. C. SHARMA, Thermal instability of compressible fluids with Hallcurrents through porous medium, Instanbul Univ. Fen. Fak. Mec. A, 43 (1978), 89-98. | MR 948330
[28] R. C. SHARMA - NEELA RANI, Hall effects on thermosolutal instability of a plasma, Indian J. of Pure Appl. Mat., 19, 2 (1988), 202-207. | Zbl 0637.76045
[29] R. C. SHARMA - TRILOK CHAND, Thermosolutal instability of compressible Hall plasma in porous medium, Astrophysics and Space Science, 155 (1989), 301-310. | Zbl 0671.76072
[30] V. A. SOLONNIKOV - G. MULONE, On the solvability of some initial boundary value problems in magnetofluidmechanics with Hall and ion-slip effects, Rend. Mat. Acc. Lincei, 9, 6 (1995), 117-132. | fulltext EuDML | MR 1354225 | Zbl 0834.76094
[31] G. W. SUTTON - A. SHERMAN, Engineering magnetohydrodynamics, Mc Graw Hill, New York, 1965.

La collezione può essere raggiunta anche a partire da EuDML, la biblioteca digitale matematica europea, e da mini-DML, il progetto mini-DML sviluppato e mantenuto dalla cellula Math-Doc di Grenoble.

Per suggerimenti o per segnalare eventuali errori, scrivete a

logo MBACCon il contributo del Ministero per i Beni e le Attività Culturali