Generalized Lieb-Thirring Inequalities and the Dimension of Attractors Associated to the Ginzburg-Landau p.d.e.
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.
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- 1.P. Constantin, Indiana University Math. J., to appear.Google Scholar
- 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
- 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
- 12.R. Temam, Infinite Dimensional Dynamical Systems in Mechanics and Physics, Springer, Berlin, to appear.Google Scholar