Upper bound on the dimension of the attractor for nonhomogeneous Navier-Stokes equations

Discrete and Continuous Dynamical Systems

Volumn 2, Issue 1, 1996, Pages 95-110

  Miranville, Alain ^a   Wang, Xiaoming ^b  

^a UNIVERSITÉ PARIS SACLAY   (France)

^b INDIANA UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038941672     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.1996.2.95     Document Type: Article

References (14)

1. P. Constantin and C. R. Doering, Energy dissipation in shear driven turbulence, Phys. Rev. Letters, 69 (1992).
2. P. Constantin, Geometric and analytic studies in turbulence, in "Trends and Perspectives in Applied Mathematics," AMS Math. Sci, 100, Springer-Verlag, New York, 1994.
3. P. Constantin, C. Foias and R. Temam, On the dimension of the attractors in two-dimensional turbulence, Physica D, 30, (1988), 284-296.
4. J.M. Ghidaghia, M. Marion and R. Temam, Generalization of the Sobolev-Lieb-Thirring inequalities and applications to the dimension of attractors, Diff. Integral Equ. 1 (1988), 1-21.
5. J.M. Ghidaglia and R. Temam, Lower bound on the dimension of the attractor for the Navier-Stokes equations in space dimension 3, in "Mechanics, Analysis and Geometry: 200 years after Lagrange" (ed. M. Francaviglia), Elsevier, Amsterdam, 1990.
6. E. Hopf, "On Linear Partial Differential Equations," Berkeley 1955, Ed. University of Kansas, 1957.
7. V.X. Liu, A sharp lower bound for the Hausdorff dimension of the global attractor of the 2D Navier-Stokes equations, Comm. Math. Phys. 158 (1993), 327-339.
8. A. Miranville, Shear layer flow in a channel: estimate on the dimension of the attractor, Physica D, 65 (1993), 135-153.
9. A. Miranville, Upper bound on the dimension of the attractor for the shear-layer flow in space dimension 3, in "Dynamical Systems: theory and applications," (ed. S.I. Andersson, A.E. Andersson and U. Ottoson), World Scientific Publishing Co, 1993.
10. R. Temam, "Navier-Stokes Equations, Theory and Numerical Analysis," 3rd edition, North-Holland, Amsterdam, 1984.
11. R. Temam, "Infinite Dimensional Dynamical Systems in Mechanics and Physics," Springer Verlag, New York, 1988.
12. R. Temam and X. Wang, Asymptotic analysis of the linearized Navier-Stokes equations in a 2D channel, to appear.
13. A.N. Kolmogorov, C.R. (Dokl.) Acad. Sci. URSS, 30, 301 (1941).
14. G.I. Taylor, Proc. R. Soc. London A 151, 421, 1935.