References
Adams, R. 1976 Sobolev spaces, Academic Press: New York.
Chandrasekhar, S. 1952 Phil. Mag. Sc. 7, 43, 501.
Chandrasekhar, S. 1961 Hydrodynamic and hydromagnetic stability, Oxford University Press.
Galdi, G. P. 1985 Arch. Rational Mech. Anal. 87, 167.
Galdi, G. P. & Straughan, B. 1985a Arch. Rational Mech. Anal. 89, 211.
Galdi, G. P. & Straughan, B. 1985b Proc. R. Soc. Lond. A 402, 257.
Hardy, G. H., Littlewood, J. E. & Polya, G. 1959 Inequalities, Cambridge University Press.
Joseph, D. D. 1965 Arch. Rational Mech. Anal. 20, 59.
Joseph, D. D. 1970 Arch. Rational Mech. Anal. 36, 285.
Joseph, D. D. 1976 Stability of fluid motions, I and II, Springer-Verlag: Berlin.
Ladyzhenskaya, O. A. 1969 Mathematical theory of viscous incompressible flow, Gordon & Breach: New York.
Rionero, S. 1968 Ricerche Mat. 17, 64.
Rionero, S. 1986 On the choice of the Lyapunov function in the fluid motion stability, lecture given at the meeting “Energy stability and convection”, Capri 21–28 May.
Rionero, S. & Mulone, G., On a maximum problem governing the non-linear stability of fluid motions, Ricerche Mat., to appear.
Serrin, J. 1959 Arch. Rational Mech. Anal. 3, 1.
Thompson, W. B. 1951 Phil. Mag. 42 (7), 1417.
Author information
Authors and Affiliations
Additional information
Communicated by K. R. Rajagopal
This research has been performed under the auspices of the G.N.F.M. of the C.N.R. and has been partially supported by the Italian Ministry for Education (M.P.I.) under 40% and 60% contracts and by C.N.R.-S,P.A.I.M.
Rights and permissions
About this article
Cite this article
Rionero, S., Mulone, G. A non-linear stability analysis of the magnetic Bénard problem through the Lyapunov direct method. Arch. Rational Mech. Anal. 103, 347–368 (1988). https://doi.org/10.1007/BF00251445
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00251445