Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



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
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  • [1] S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, Oxford University Press, Oxford, 1961
  • [2] S. H. Davis, On the principle of exchange of stabilities, Proc. Roy. Soc. London Ser. A 310, 341-358 (1969)
  • [3] G. P. Galdi, Nonlinear stability of the magnetic Bénard problem via a generalized energy method, Arch. Rational Mech. Anal. 87, 167-186 (1985)
  • [4] G. P. Galdi and B. Straughan, Exchange of stabilities, symmetry and nonlinear stability, Arch. Rational Mech. Anal. 89, 211-228 (1985a)
  • [5] 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)
  • [6] 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)
  • [7] D. D. Joseph, On the stability of Boussinesq equations, Arch. Rational Mech. Anal. 20, 59-71 (1965)
  • [8] D. D. Joseph, Nonlinear stability of Boussinesq equations by the method of energy, Arch. Rational Mech. Anal. 22, 163-184 (1966)
  • [9] D. D. Joseph, Stability of fluid motion. Vols. I, II, Springer-Verlag, Berlin, Heidelberg and New York, 1976
  • [10] 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)
  • [11] 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)
  • [12] 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)
  • [13] S. Rionero, Metodi variazionali per la stabilità asintotica in media in magnetoidrodinamica, Ann. Mat. Pura Appl. (4) 78, 339-364 (1968)
  • [14] 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)
  • [15] J. Serrin, On the stability of viscous fluid motion, Arch. Rational Mech. Anal. 3, 1-13 (1959)
  • [16] K. Walker and G. M. Homsy, A note on convective instability in Boussinesq fluids and porous media, J. Heat Transfer 99, 338-339 (1977)
  • [17] D. R. Westbrook, The stability of convective flow in a porous medium, Phys. Fluids 12, 1547-1551 (1969)

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DOI: https://doi.org/10.1090/qam/1315452
Article copyright: © Copyright 1995 American Mathematical Society

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