Bibliography
Adams, R. A., (1975), Sobolev Spaces, Academic Press, N.Y., S. Francisco, London.
Agmon, S., Douglis, A., & L. Nirenberg, (1959), Comm. Pure Appl. Math., 12, 623.
Agrawal, S. C., (1969), J. Phys. Soc. Japan, 26, 561.
Aris, R., (1975), The Mathematical Theory of Diffusion and Reaction in Permeable Catalysts, Vol. II, Oxford.
Babovsky, H., & M. Padula (forthcoming), New contributions to nonlinear stability of a discrete velocity model.
Banerjee, M. B., Gupta, J. R., Shandil, R. G., & S. K. Sood, (1985), J. Math. Anal. and Appl., 108, 216.
Bogovskii, M. E., (1979), Soviet Math. Dokl., 20, 1094.
Braginskii, S. I., (1957), J. Exptl. Theoret. Phys., 33, 459.
Busse, F. H., (1975), J. Fluid Mech., 71, 193.
Cattabriga, L., (1961), Rend. Mat. Sem. Univ. Padova, 31, 308.
Chandrasekhar, S., (1981), Hydrodynamic and Hydromagnetic Stability, Dover Publ. Inc., N.Y.
Chandrasekhar, S., & D. D. Elbert, (1955), Proc. Roy. Soc. London (A), 231, 198.
Coscia, V., & M. Padula, (1989), Hydrosoft, 2 (4), 182.
Coscia, V., & M. Padula, (1990), Geophys. Astrophys. Fluid Dyn., in press.
Cowling, T. G., (1957), Magnetohydrodynamics, Intersci. N.Y.
Donnelly, R. J., & M. Ozima, (1960), Phys. Rev. Letters, 4, 497.
Drazin, P. G., & W. H. Reid, (1982), Hydrodynamic Stability, Cambridge Monographs on Mech. and Appl. Math., Cambridge Univ. Press.
Ebin. D., & M. C. Shen, (1987), J. Math. Anal. and Appl., 125, 81.
Ebin, D., & M. C. Shen, (1988), Ann. Mat. Pura Appl., 50, 39.
Fife, P., (1979), Mathematical Aspects of Reacting and Diffusing Systems, Springer Lecture Notes in Mathematics, 28.
Galdi, G. P., (1975), Arch. Rational Mech. Anal., 59, 1.
Galdi, G. P., (1979), Ricerche Mat., 27, 387.
Galdi, G. P., (1985), Arch. Rational Mech. Anal., 87, 167.
Galdi, G. P., (1989), Proc. Fourth Intl Conf. on Computational Methods and Experimental Measurements, Eds. G. M. Carlomagno & C. A. Brebbia, Springer-Verlag Berlin Heidelberg N. Y. London Paris Tokyo, 183.
Galdi, G. P., An Introduction to the Mathematical Theory of the Navier-Stokes Equations, Springer Tracts in Natural Philosophy, forthcoming.
Galdi, G. P., & I. Herron, (1985), Quart. Appl. Math., 52, 159.
Galdi, G. P., & M. Padula, (1990), Proc. Third Workshop on Math. Aspects of Fluids and Plasma Dynamics, G. Toscani, V. Boffi & S. Ronero Eds., Springer Lecture Notes in Math., in Press.
Galdi, G. P., & S. Rionero, (1985), Weighted Energy Methods in Fluid Dynamics and Elasticity, Springer Lecture Notes in Mathematics, 1134
Galdi, G. P., & B. Straughan, (1985a), Arch. Rational Mech. Anal., 89, 211.
Galdi, G. P., & B. Straughan, (1985b), Proc. Roy. Soc. London (A), 402, 257.
Galdi, G. P., Payne, L. H., Proctor, M. R. E., & B. Straughan, (1987), Proc. Roy. Soc. London (A), 414, 83.
Galdi, G. P., Padula, M., & K. R. Rajagopal, (1990), Arch. Rational Mech. Anal., 109, 173.
Gavalas, G. R., (1968), Nonlinear Differential Equations of Chemically Reacting Systems, Springer-Verlag, N.Y.
Glazman, I. M., (1965), Direct Methods of Qualitative Spectral Analysis of Singular Differential Operators, Israel Progr. for Sci. Transl., Jerusalem.
Goody, R. M., (1956), J. Fluid Mech., 1, 424.
Guckenheimer, J., & E. Knobloch, (1983), Geophys. Astrophys. Fluid Dyn., 23, 247.
Henry, D., (1981), Geometric Theory of Semilinear Parabolic Equations, Springer Lecture Notes in Mathematics, 840.
Hetrick, D. L., (1971), Dynamics of Nuclear Reactors, Univ. Chicago Press, Chicago.
Heywood, J. G., (1980), Indiana Univ. Math. J., 21, 639.
Kadish, A., (1976), Phys. Fluids, 19, 141.
Kappraff, J., Grossmann, W., & M. Dress, (1981), J. Plasma Physics, 25, 111.
Kato, T., (1966), Perturbation Theory for Linear Operators, Springer-Verlag, Berlin, Heidelberg, N. Y.
Kaufman, A., (1960), La Théorie des Gas Neutres et Ionizés, Herman et Cie., Paris.
Kloeden, P., & R. Wells, (1983), Proc. Roy. Soc. London (A), 390, 293.
Kolyshkin, A. A., (1987), Magnitnaya Gidrodinamika, 1, 67 (in Russian).
Krishnamurthy, R., (1967), Ph. D. Thesis, Dept. Geophysics and Planetary Science, UCLA.
Jorné, J., & S. Carmi, (1977), Math. Biosciences, 37, 51.
Joseph, D. D., (1965), Arch. Rational Mech. Anal, 20, 59.
Joseph, D. D., (1966), Arch. Rational Mech. Anal., 22, 163.
Joseph, D. D., (1970), Arch. Rational Mech. Anal., 36, 285.
Joseph, D. D., (1976), Stability of Fluid Motions, Springer Tracts in Natural Philosophy, Volumes I and II.
Ladyzhenskaya, O. A., (1969), The Mathematical Theory of Viscous Incompressible Flow, Gordon & Breach Sci. Publ., N. Y., London, Paris.
Langlois, W. E., (1981), Physico-Chem. Hydrodyn., 2, 245.
Liubimov, H. A., (1962), J. Mech. Appl. Math. (PMM), 26, 789.
Maiellaro, M., & L. Palese, (1984), Int. J. Engng. Sci., 22, 411.
Zaremonti, P., (1984), Rend. Sem. Mat. Univ. Padova, 71, 35.
Masuda, K., (1975), J. Math. Soc. Japan, 27, 294.
Mattei, G., (1970), Ann. Mat. Pura Appl., 80, 1.
Miklavčic, M., (1985), Pacific J. of Math., 118, 199.
Mulone, G., & S. Rionero, (1988), J. Math. Anal. and Appl., in Press.
Nečas, J., (1967), Les Méthodes Directes en Théorie des Equations Elliptiques, Masson et Cie., Prague.
Nicolis, G., & I. Prigogine, (1977), Self Organization in Nonequilibrium Systems, John Wiley & Sons Inc., N.Y., London, Sydney, Toronto.
Orr, W. McF., (1907), Proc. Roy. Irish Acad. (A), 27, 69.
Padula, M., (1984), Proc. Roy. Soc. Edinburgh, 96, 55.
Padula, M., (1986), Boll. U.M.I., 5B, 581.
Padula, M., (1988a), Energy Instability Methods: an Application to Burgers Equation, Proc. Meeting Energy Stability and Convection, Galdi, G. P., & B. Straughan Eds., Pitman Research Notes in Mathematics, 168.
Padula, M., (1988b), Compressible Convection: Nonlinear Results, Proc. Intl. Conf. on “Mathematical Modelling in Science and Technology”, Madras, India.
Padula, M., (1990), Proc. Conf. on Waves and Stability in Continuous Media, S. Rionero Ed., World Sci. Publ., in Press.
Peckover, R. S., & N. O. Weiss, (1972), Comp. Phys. Comm., 4, 339.
Proctor, M. R. E., & D. J. Galloway, (1979), J. Fluid Mech., 90, 273.
Proctor, M. R. E., & N. O. Weiss, (1982), Rep. Progr. Phys., 45, 1317.
Rai, L., (1968), J. Phys., 46, 2533.
Rayleigh, Lord, (1916), Proc. Roy. Soc. London (A), 93, 148.
Reynolds, O., (1895), Phil. Trans. Roy. Soc. London (A), 186, 123.
Rionero, S., (1968), Ann. Mat. Pura Appl., 78, 339.
Rionero, S., (1971), Ricerche Mat., 20, 285.
Rionero, S., (1988), On the Choice of the Liapunov Functional in the Stability of Fluid Motions, Proc. Meeting “Energy Stability and Convection”, Galdi, G. P., & B. Straughan Eds., Pitman Research Notes in Mathematics, 168.
Rionero, S., & G. Mulone, (1988), Arch. Rational Mech. Anal., 103, 347.
Roberts, P. H., (1964), Proc. Camb. Phil. Soc., 60, 635.
Roberts, P. H., (1967a), An Introduction to Magnetohydrodynamics, Longmans: London.
Roberts, P. H., (1967b), J. Fluid Mech., 30, 33.
Roberts, P. H., & K. Stewartson, (1974), Phil. Trans. Roy. Soc. Lond. (A), 277, 287.
Rossby, H. T., (1969), J. Fluid Mech., 36, 306.
Rudraiah, N., (1981), Publ. Astron. Soc. Japan, 33, 721.
Rudraiah, N., Kumudini, V., & W. Unno, (1985), Publ. Astron. Soc. Japan, 37, 183.
Rudraiah, N., & M. Sekhar, (1988), Effect of Non-uniform Temperature Gradient on Convection in Magnetic Fluids, preprint of the Central College, Bangalore.
Sattinger, D. S., (1973), Topics in Stability and Bifurcation Theory, Springer Lect. Notes in Math., 309, Berlin, Heidelberg, N. Y.
Segel, L. A., & J. L. Jackson, (1972), J. Theor. Biol., 37, 545
Serrin, J., (1959), Arch. Rational Mech. Anal., 3, 1.
Solonnikov, V. A., & Y. Scadilov, (1973), Trudy Mat. Inst. Steklov, 125, 186.
Solonnikov, V. A., & D. Pileckas, (1986), J. Soviet Mat., 34, 2101.
Sparrow, E. M., Goldstein, R. J., & V. K. Jonsson, (1964), J. Fluid Mech., 18, 513.
Spitzer, J., (1964), Physics of Fully Ionized Gases, Intersci. Tracts on Phys. and Astron.
Straughan, B., (1982), Portugaliae Matematica, 41, 251.
Straughan, B., (1988), Convection in a variable gravity field, preprint of Univ. Glasgow
Synge, J. L., (1933), Trans. of the Royal Society of Canada, 27, 1.
Thompson, W. B., (1951), Phil. Mag., 42, 1417.
Veronis, G., (1959), J. Fluid Mech., 5, 401.
Weiss, N. O., (1981), J. Fluid Mech., 108, 247.
Youdovich, V. I., (1967), Math. USSR Sbornik, 3, 519.
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Communicated by K. R. Rajagopal
Dedicated to Clifford Truesdell, on his 70th birthday
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Galdi, G.P., Padula, M. A new approach to energy theory in the stability of fluid motion. Arch. Rational Mech. Anal. 110, 187–286 (1990). https://doi.org/10.1007/BF00375129
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DOI: https://doi.org/10.1007/BF00375129