Nonlinear stability of the rotating Bénard problem, the case Pr = 1

Nonlinear Differential Equations and Applications

Volumn 5, Issue 3, 1998, Pages 283-307

  Kaiser, Ralf ^a   Xu, L X ^a  

^a UNIVERSITY OF BAYREUTH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0004413456     PISSN: 10219722     EISSN: None     Source Type: Journal    
DOI: 10.1007/s000300050047     Document Type: Article

References (16)

1. S. CHANDRASEKHAR, Hydrodynamic and hydromagnetic stability, Dover, New York, 1981
2. G. P. GALDI, Nonlinear stability of the magnetic Bénard problem via a generalized energy method, Arch. Rational Mech. Anal. 87, 167-186 (1985)
3. G. P. GALDI, M. PADULA, A new approach to energy theory in the stability of fluid motion, Arch. Rational Mech. Anal. 110, 187-286 (1990)
4. G. P. GALDI, B. STRAUGHAN, A nonlinear analysis of the stabilizing effect of rotation in the Bénard problem, Proc. Roy. Soc. London Ser. A 402, 257-283 (1985)
5. G. H. HARDY, J. E. LITTLEWOOD, G. POLYA, Inequalities, Cambridge University Press, 1934
6. D. D. JOSEPH, Global stability of the conduction-diffusion solution, Arch. Rational Mech. Anal. 36, 285-292 (1970)
7. Y. KAGEI, W. von WAHL, Asymptotic stability of higher order norms in terms of asymptotic energy stability for viscous incompressible fluid flows heated from below, Japan J. Indust. Appl. Math. 13, 33-49 (1996)
8. R. KAISER R., W. von WAHL, Stability of plane parallel shear flow in a rotating layer heated from below, to appear in Calc. of Var. (1997)
9. G. MULONE, S. RIONERO, On the nonlinear stability of the rotating Bénard problem via the Lyapunov direct method, J. Math. Anal. and Appl. 144, 109-127 (1989)
10. A. J. PRITCHARD, A study of the classical problems of hydrodynamic stability by the Lyapunov method, J. Inst. Math. Appl. 4, 78-93 (1968)
11. H. T. ROSSBY, A study of Bénard convection with and without rotation, J. Fluid Mech. 36, 309-335 (1969)
12. B. J. SCHMITT, private communication (1997)
13. B. J. SCHMITT, W. von WAHL, Decomposition of solenoidal fields into poloidal fields, toroidal fields and the mean flow. Applications to the Boussinesq-equations, in The Navier-Stokes Equations II - Theory and Numerical Methods, Lecture Notes in Mathematics 1530, 291-305, Springer: Berlin, Heidelberg, New York, 1992
14. W. von Wahl, The Boussinesq-equations in terms of poloidal and toroidal fields and the mean flow. Lecture Notes, Bayreuther Math. Schr. 40, 203-290 (1992)
15. W. von WAHL, Necessary and sufficient conditions for the stability of flows of incompressible viscous fluids, Arch. Rational Mech. Anal. 126, 103-129 (1994)
16. W. von WAHL, private communication (1996)