Abstract
This paper is part I of a limited review of the applications of the spectral theory of linear operators in an astrophysical context. The ideal magnetohydrodynamic equations arise in the study of magnetic flux tubes in the solar corona, and in the plasma physics of nuclear containment devices. The system described by these equations is very rich both mathematically and physically, and there are many open problems associated with these models. The underlying mathematical principles are discussed in a qualitative manner in Paper I, and in a more technical manner in subsequent Paper II.
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References
Adam, J. A.: 1978a,Quart. J. Mech. Appl. Math. 31, 77.
Adam, J. A.: 1978b,J. Plasma Phys. 19, 77.
Adam, J. A.: 1980,J. Phys. A. Math. Gen. 13, 3325.
Adam, J. A.: 1982,Int. J. Math. Ed. Sci. Technol. 13, 405.
Adam, J. A.: 1984,Int. J. Math. Ed. Sci. Technol. 15, 672.
Adam, J. A.: 1985,Astrophys. Space Sci. 114, 249.
Adam, J. A.: 1986a,Phys. Rep. 142, 263.
Adam, J. A.: 1986b,Astrophys. Space Sci. (in press).
Adam, J. A.: 1987,Wave Motion (submitted).
Agrawal, G. S.: 1969,J. Phys. Soc. Japan 26, 1519.
Bernstein, I. B., Frieman, E. A., Kruskal, M. D., and Kulsrud, R. M.: 1958,Proc. Roy. Soc. London 244A, 17.
Chadrasekhar, S.: 1961,Hydrodynamic and Hydromagnetic Stability, Clarendon Press, Oxford.
Chimonas, G.: 1970,J. Fluid Mech. 43, 833.
Cally, P. S.: 1983,Geophys. Astrophys. Fluid Dynamics 23, 43.
Cally, P. S. and Adam, J. A.: 1983,Geophys. Astrophys. Fluid Dynamics 23, 57.
Dyson, J. and Schutz, B. F.: 1979,Proc. Roy. Soc. London A368, 389.
Friedrichs, K. O.: 1958,Comm. Pure Applied Math. 2, 333.
Frieman, E. and Rotenberg, M.: 1960,Rev. Mod. Phys. 32, 898.
Goedbloed, J. P.: 1974, Unpublished report, Courant Inst. of Math. Sciences
Goedbloed, J. P.: 1975,Phys. Fluids 18, 1258.
Goedbloed, J. P.: 1983,Lecture Notes on Ideal Magnetohydrodynamics, Rijnhuizen Report 83-145, Nieuwegein, Holland.
Goedbloed, J. P. and Sakanaka, P. H.: 1974,Phys. Fluids 17, 908.
Grad, H.: 1966,Phys. Fluids 9, 225.
Hameiri, E.: 1979,Phys. Fluids 22, 89.
Hameiri, E.: 1981,Phys. Fluids 24, 562.
Hameiri, E.: 1985,Comm. Pure Appl. Math. 38, 43.
Hameiri, E. and Hammer, J. H.: 1979,Phys. Fluids 22, 1700.
Howard, L. N.: 1961,J. Fluid Mech.,10, 509.
Ionson, J. A.: 1978,Astrophys. J. 226, 650.
Hochhar, G. I. and Jain, R. K.: 1979,J. Fluid Mech. 91, 489.
Laurence, P. and Shen, M. C.: 1983,Comm. Pure Applied Math. 36, 233.
Lawrence, P.: 1986,J. Math. Phys. 27, 1916.
Laval, G., Mercier, C. and Pellat, R.: 1965,Nucl. Fusion 5, 156.
Pridmore-Brown, D. C.: 1966,Phys. Fluids 9, 1290.
Rae, I. N. and Roberts, B.: 1982,Monthly Notices Roy. Astron. Soc. 201, 1171.
Sedláček, Z.: 1971,J. Plasma Phys. 5, 239.
Tataronis, J. and Grossman, W.: 1973,Z. Phys. 261, 203.
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Adam, J.A. Spectral theory and stability in astrophysics. Astrophys Space Sci 127, 163–178 (1986). https://doi.org/10.1007/BF00637772
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DOI: https://doi.org/10.1007/BF00637772