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    Fife, P. C. and Joseph, D. D. 1969. Existence of convective solutions of the generalized Bénard problem which are analytic in their norm. Archive for Rational Mechanics and Analysis, Vol. 33, Issue. 2, p. 116.
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    Joseph, Daniel D. 1965. On the stability of the Boussinesq equations. Archive for Rational Mechanics and Analysis, Vol. 20, Issue. 1, p. 59.
    Platzman, George W. 1965. The spectral dynamics of laminar convection. Journal of Fluid Mechanics, Vol. 23, Issue. 03, p. 481.
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On the non-existence of subcritical instabilities in fluid layers heated from below

  • R. Sani (a1) (a2)
Abstract

Using some recent results it is established that, for very general boundary conditions, time-independent subcritical instabilities do not exist for the non-linear thermoconvective stability problem.

Copyright
© 1964 Cambridge University Press
References
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Ladyzhenskaya, O. A. 1963 The Mathematical Theory of Viscous Incompressible Flow. New York: Gordon and Breach.
Phillips, H. B. 1933 Vector Analysis. New York: John Wiley.
Sani, R. L. & Scriven, L. E. 1964 Convective instability. I. To be submitted to Phys. Fluids.
Stuart, J. T. 1960 Non-linear effects in hydrodynamic stability. Proc. X-th Int. Congr. Appl. Math. pp. 63–97. Stresa, Elsevier.
Stuart, J. T. 1960 On the nonlinear mechanics of wave disturbances in stable and unstable parallel flow, I. J. Fluid Mech. 9, 353–70.
Ukhovskii, M. R. & Iudovich, V. I. 1963 On the equations of steady-state convection. Prik. Math. Mek. 27, 432–40.
Watson, J. 1960 On the nonlinear mechanics of wave disturbances in stable and unstable parallel flows, II. J. Fluid Mech. 9, 371–89.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
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