Nonlinear stability problem of a rotating porous layer
Authors:
Y. Qin and P. N. Kaloni
Journal:
Quart. Appl. Math. 53 (1995), 129-142
MSC:
Primary 76E30; Secondary 35Q35, 76E15, 76S05, 76U05
DOI:
https://doi.org/10.1090/qam/1315452
MathSciNet review:
MR1315452
Full-text PDF Free Access
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Additional Information
S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, Oxford University Press, Oxford, 1961
S. H. Davis, On the principle of exchange of stabilities, Proc. Roy. Soc. London Ser. A 310, 341–358 (1969)
G. P. Galdi, Nonlinear stability of the magnetic Bénard problem via a generalized energy method, Arch. Rational Mech. Anal. 87, 167–186 (1985)
G. P. Galdi and B. Straughan, Exchange of stabilities, symmetry and nonlinear stability, Arch. Rational Mech. Anal. 89, 211–228 (1985a)
G. P. Galdi and B. Straughan, A nonlinear analysis of the stabilizing effect of rotation in the Bénard problem, Proc. Roy. Soc. London Ser. A 402, 257–283 (1985b)
G. P. Galdi and M. Padula, A new approach to energy theory in the stability of fluid motion, Arch. Rational Mech. Anal. 110, 187–286 (1990)
D. D. Joseph, On the stability of Boussinesq equations, Arch. Rational Mech. Anal. 20, 59–71 (1965)
D. D. Joseph, Nonlinear stability of Boussinesq equations by the method of energy, Arch. Rational Mech. Anal. 22, 163–184 (1966)
D. D. Joseph, Stability of fluid motion. Vols. I, II, Springer-Verlag, Berlin, Heidelberg and New York, 1976
G. Mulone and S. Rionero, On the nonlinear stability of the rotating Bénard problem via the Lyapunov direct method, J. Math. Anal. Appl. 144, 109–127 (1989)
W. McF. Orr, The stability or instability of the steady motions of perfect liquid and of a viscous liquid, Proc. Roy. Irish Acad. A27, 9–68 and 69–138 (1907)
Y. Qin and P. N. Kaloni, Steady convection in a porous medium based upon the Brinkman model, IMA J. Appl. Math. 35, 85–95 (1992)
S. Rionero, Metodi variazionali per la stabilità asintotica in media in magnetoidrodinamica, Ann. Mat. Pura Appl. (4) 78, 339–364 (1968)
S. Rionero and B. Straughan, Convection in a porous medium with internal heat source and variable gravity effects, Internat. J. Engrg. Sci. 28, 497–503 (1990)
J. Serrin, On the stability of viscous fluid motion, Arch. Rational Mech. Anal. 3, 1–13 (1959)
K. Walker and G. M. Homsy, A note on convective instability in Boussinesq fluids and porous media, J. Heat Transfer 99, 338–339 (1977)
D. R. Westbrook, The stability of convective flow in a porous medium, Phys. Fluids 12, 1547–1551 (1969)
S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, Oxford University Press, Oxford, 1961
S. H. Davis, On the principle of exchange of stabilities, Proc. Roy. Soc. London Ser. A 310, 341–358 (1969)
G. P. Galdi, Nonlinear stability of the magnetic Bénard problem via a generalized energy method, Arch. Rational Mech. Anal. 87, 167–186 (1985)
G. P. Galdi and B. Straughan, Exchange of stabilities, symmetry and nonlinear stability, Arch. Rational Mech. Anal. 89, 211–228 (1985a)
G. P. Galdi and B. Straughan, A nonlinear analysis of the stabilizing effect of rotation in the Bénard problem, Proc. Roy. Soc. London Ser. A 402, 257–283 (1985b)
G. P. Galdi and M. Padula, A new approach to energy theory in the stability of fluid motion, Arch. Rational Mech. Anal. 110, 187–286 (1990)
D. D. Joseph, On the stability of Boussinesq equations, Arch. Rational Mech. Anal. 20, 59–71 (1965)
D. D. Joseph, Nonlinear stability of Boussinesq equations by the method of energy, Arch. Rational Mech. Anal. 22, 163–184 (1966)
D. D. Joseph, Stability of fluid motion. Vols. I, II, Springer-Verlag, Berlin, Heidelberg and New York, 1976
G. Mulone and S. Rionero, On the nonlinear stability of the rotating Bénard problem via the Lyapunov direct method, J. Math. Anal. Appl. 144, 109–127 (1989)
W. McF. Orr, The stability or instability of the steady motions of perfect liquid and of a viscous liquid, Proc. Roy. Irish Acad. A27, 9–68 and 69–138 (1907)
Y. Qin and P. N. Kaloni, Steady convection in a porous medium based upon the Brinkman model, IMA J. Appl. Math. 35, 85–95 (1992)
S. Rionero, Metodi variazionali per la stabilità asintotica in media in magnetoidrodinamica, Ann. Mat. Pura Appl. (4) 78, 339–364 (1968)
S. Rionero and B. Straughan, Convection in a porous medium with internal heat source and variable gravity effects, Internat. J. Engrg. Sci. 28, 497–503 (1990)
J. Serrin, On the stability of viscous fluid motion, Arch. Rational Mech. Anal. 3, 1–13 (1959)
K. Walker and G. M. Homsy, A note on convective instability in Boussinesq fluids and porous media, J. Heat Transfer 99, 338–339 (1977)
D. R. Westbrook, The stability of convective flow in a porous medium, Phys. Fluids 12, 1547–1551 (1969)
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Article copyright:
© Copyright 1995
American Mathematical Society
