References
- Adams , R. 1975 . Sobolev Spaces , New York : Academic Press .
- Carmi , S. and Joseph , D. D. 1966 . “Subcritical convective instability II: Spherical shells” . J. Fluid Mech. , 26 : 769
- Chandrasekhar , S. 1961 . Hydrodynamic and Hydromagnetic Stability , Oxford : University Press .
- Coscia , V. and Padula , M. 1989 . “Quantitative bounds for nonlinear stability in compressible Bénard problem” . Hydrosoft , 2 : 182
- Coscia , V. and Padula , M. “Accurate numerical procedures for nonlinear stability in a compressible atmosphere” . (in preparation)
- Courant , R. and Freidrichs , K. O. 1948 . Supersonic Flow and Shock Waves , Intersciences Publisher .
- Davis , S. H. 1969 . “Buoyancy-surface tension instability by the method of energy” . J. Fluid Mech. , 39 : 347
- Davis , S. H. 1969 . “On the principle of exchange of stabilities” . Proc. R. Soc Lond. , A310 : 341
- Galdi , G. P. 1985 . “Nonlinear-stability of the magnetic Bénard problem via a generalized energy method” . Arch. Rational Mech. Anal. , 87 : 167
- Galdi , G. P. and Padula , M. 1990 . “A new approach to energy theory in the stability of fluid motion” . Arch. Rational Mech. Anal. , in press
- Galdi , G. P. and Straughan , B. 1985a . “Exchange of stabilities, symmetry and nonlinear stability” . Arch. Rational Mech. Anal. , 89 : 211
- Galdi , G. P. and Straughan , B. 1985b . “A nonlinear analysis of the stabilizing effects of rotation in the Bénard problem” . Proc. R. Soc. Lond. , A402 : 257
- Galdi , G. P. , Padula , M. and Rajagopal , K. R. 1990 . “On the conditional stability of the rest state of a fluid of second grade in unbounded domains” . Arch. Rational Mech. Anal. , 109 : 173
- Goudet , G. 1954 . Les Fonctions de Bessel , Paris : Massons et Cie .
- Gough , D. O. , Moore , D. R. , Spiegel , E. A. and Weiss , N. O. 1976 . “Convective instability in a compressible atmosphere II” . Ap. J. , 206 : 536
- Graham , E. 1975 . “Numerical simulation of two-dimensional compressible convection” . J. Fluid Mech. , 70 : 689
- Jeffreys , H. 1930 . “The instability of a compressible fluid heated from below” . Proc. Cam. Phil. Soc. , 26 : 170
- Joseph , D. D. 1965 . “On the stability of the Boussinesq equation” . Arch. Rational Mech. Anal. , 20 : 59
- Joseph , D. D. 1966 . “Nonlinear stability of the Boussinesq equation by the method of energy” . Arch. Rational Mech. Anal. , 22 : 163
- Joseph , D. D. 1976 . Stability of Fluid Motion , Berlin : Springer Verlag .
- Joseph , D. D. and Shir , C. C. 1966 . “Subcritical convective instability I: Fluid layers” . J. Fluid Mech. , 26 : 753
- Ladyzhenskaja , O. A. 1985 . The Boundary Value Problems of Mathematical Physics , Berlin : Springer Verlag .
- Malkus , W. V. R. 1954 . “The heat transport and spectrum of thermal turbulence” . Proc. R. Soc. Lond. , 225 : 185
- Malkus , W. V. R. and Veronis , G. 1958 . “Finite amplitude cellular convection” . J. Fluid Mech. , 4 : 255
- Matsumura , A. and Nishida , T. 1980 . “The initial value problem for the equation of motion of viscous and heat conducting gases” . J. Math. Kyoto Univ. , 20 : 67
- Mulone , G. and Rionero , S. 1989 . “On the nonlinear stability of the rotating Bénard problem via the Lyapunov direct method” . J. Math. Anal. Appl. , 144 : 109
- Necas , J. 1976 . Les Methods Directed en Theorie des Equations Elliptiques , Paris : Massons et Cie .
- Padula , M. and Bollettino , U. M. I. 1986 . “Nonlinear energy stability for the compressible Bénard problem” . 5B : 581
- Pellew , A. and Southwell , R. V. 1940 . “On maintained convective motion in a fluid heated from below” . Proc. R. Soc. Lond. , A176 : 312
- Proctor , M. R. E. and Weiss , N. O. 1982 . “Magnetoconvection” . Rep. Progr. Phys. , 45 : 1317
- Rayleigh , Lord. 1916 . “On convective currents in a horizontal layer of fluid when the higher temperature is on the under side” . Phil. Mag. , 32 : 529
- Rionero , S. and Mulone , G. 1988 . “A nonlinear stability analysis of the magnetic Bénard problem through the Lyapunov direct method” . Arch. Rational Mech. Anal. , 103 : 347
- Roberts , P. H. 1968 . “On the thermal instability of a rotating fluid sphere containing heat sources” . Phil. Trans. R. Soc. Lond. , A236 : 93
- Roberts , P. H. and Stewartson , K. 1974 . “On finite amplitude convection in a rotating magnetic system” . Phil. Trans. R. Soc. Lond. , A277 : 287
- Serrin , J. 1959 . “On the stability of viscous fluid motion” . Arch. Rational Mech. Anal. , 3 : 1
- Spiegel , E. A. 1958 . Dissertation , University of Michigan .
- Spiegel , E. A. 1965 . “Convective instability in a compressible atmosphere I” . Ap. J. , 141 : 4068
- Spiegel , E. A. 1971 . “Convection in stars I” . Ann. Rev. A. Ap. , 9 : 323
- Spiegel , E. A. 1972 . “Convection in stars II” . Ann. Rev. A. Ap. , 10 : 261
- Spiegel , E. A. and Veronis , G. 1960 . “On the Boussinesq approximation for a compressible fluid” . Ap. J. , 131 : 442
- Unno , W. , Kato , S. and Makita , M. 1960 . “Convective instability in polytropic atmosphere I” . Pub. Astr. Soc. Japan , 12 : 192
- Valli , A. 1986 . “Navier-Stokes equations for compressible fluids: Global estimates and periodic solutions” . In Proc. Sympos. Pure Maths. 45 Providence, RI, , USA Part 2