On the dimension of the attractor for the Benard problem with free surfaces

Russian Journal of Mathematical Physics

Volumn 5, Issue 4, 1997, Pages 489-502

  Miranville, A ^a   Ziane, M ^b  

^a UNIVERSITÉ DE POITIERS   (France)

^b INDIANA UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031320856     PISSN: 10619208     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (11)

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2. Constantin, P., Foiaş, C. and Temam, R., 'On the dimension of the attractors in two-dimensional turbulence', Physica D vol. 30 (1988), 284-296.
3. Foiaş, C., Manley, O., and Temam, R., 'Attractors for the Bénard problem: existence and physical bounds on their fractal dimensions', Nonlinear Analysis vol. 11 (1987), 938-967.
4. Ghidaglia, J. M., Marion, M., and Temam, R., 'Generalization of Sobolev-Lieb-Thirring inequalities and applications to the dimension of attractors', Differ. Integral Equat. vol. 1 (1988), 1-21.
5. Ghidaglia, J. M. and Temam, R., 'Lower bound on the dimension of the attractor for the Navier Stokes equations in space dimension 3', Mechanics, Analysis and Geometry: 200 Years After Lagrange (M. Francaviglia and D. Holmes, eds.).
6. Liu, V. X., 'A sharp lower bound for the Hausdorff dimension of the global attractors of the 2D Navier-Stokes equations', Comm. Math. Phys. vol. 158 (1993), 327-339.
7. Miranville, A., 'Lower bound on the dimension of the attractor for the Bénard problem with free surfaces', Nonlinear Analysis vol. 25 (1995), 1079-1094.
8. Temam, R. (1988), Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Springer-Verlag, New York.
9. Temam, R. and Ziane, M., 'Navier-Stokes equations in three-dimensional thin domains with various boundary conditions', Advances in Differential Equations vol. 1 (1996), 499-546.
10. Ziane, M., 'On the 2D-Navier-Stokes equations with the free boundary condition', J. Applied Math and Optimization (to appear).
11. _, 'Optimal bounds on the dimension of the attractors of Navier-Stokes equations', Physica D (to appear).