Advertisement

Generalized Lieb-Thirring Inequalities and the Dimension of Attractors Associated to the Ginzburg-Landau p.d.e.

  • J.-M. Ghidaglia
Conference paper

Abstract

This paper is concerned with the dimension of the global attractor that describes the long time behavior of the solutions to the 2D-Ginzburg-Landau partial differential equation. An upper bound on this dimension is derived via a generalized Lieb-Thirring inequality, while lower bounds follow from the classical (linear) stability analysis. As a matter of fact these bounds are of the same order and therefore optimal.

Keywords

Fractal Dimension Lyapunov Exponent Global Attractor Usual Sobolev Space Dimensional Dynamical System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    P. Constantin, Indiana University Math. J., to appear.Google Scholar
  2. 2.
    P. Constantin, C. Foias and R. Temam, Mem. Amer. Math. Soc., 53, 314 (1985),MathSciNetGoogle Scholar
  3. 2a.
    P. Constantin, C. Foias and R. Temam, see also J. Fluid Mech., 150, 427–440 (1985).CrossRefMATHADSMathSciNetGoogle Scholar
  4. 3.
    C.R. Doering, J.D. Gibbon, D.D. Holm and B. Nicolaenko, Los Alamos preprint LA-UR; 87–1546, to be published.Google Scholar
  5. 4.
    J.M. Ghidaglia and B. Héron, Physica 28 D, 282–304 (1987).ADSGoogle Scholar
  6. 5.
    J.M. Ghidaglia, M. Marion and R. Temam, Differential and Integral Equations, 1, 1–21 (1988).MATHMathSciNetGoogle Scholar
  7. 6.
    J.M. Ghidaglia and R. Temam, Asymptotic Analysis, 1,23–49 (1988).MATHMathSciNetGoogle Scholar
  8. 7.
    P. Huerre, in Equations aux Dérivées Partielles non Linéaires et Systèmes Dynamiques, J.M. Ghidaglia and J.C. Saut Ed., Travaux en cours, Hermann, Paris, 1988.Google Scholar
  9. 8.
    L. Keefe, Phys. Fluids, 29, 3135–3141 (1986).CrossRefMATHADSMathSciNetGoogle Scholar
  10. 9.
    L. Keefe, Stud. in Appl. Math., 73, 91–153 (1985).MATHADSMathSciNetGoogle Scholar
  11. 10.
    H.T. Moon, P. Huerre and L.G. Redekopp, Phys. Rev. Lett., 49, 458–460 (1982).CrossRefADSMathSciNetGoogle Scholar
  12. 11.
    H.T. Moon, P. Huerre and L.G. Redekopp, Physica 7D, 135–150 (1983).ADSMathSciNetGoogle Scholar
  13. 12.
    R. Temam, Infinite Dimensional Dynamical Systems in Mechanics and Physics, Springer, Berlin, to appear.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • J.-M. Ghidaglia
    • 1
  1. 1.Laboratoire d’Analyse NumériqueCNRS et Université Paris-SudOrsay CédexFrance

Personalised recommendations