M. Bartuccelli, J.D. Gibbon, and M. Oliver,
Length scales in solutions of the complex Ginzburg-Landau equation,
Physica D 89 (1996), 267-286.

Abstract:

We generalise and in certain cases improve on previous a priori estimates of Sobolev norms of solutions to the generalised complex Ginzburg-Landau equation. A set of dynamic length scales based on ratios of these norms is defined. We are able to derive lower bounds for time averages and long-time limits of these length scales. The bounds scale like the inverses of our Linfinity bounds.
Download the paper in postscript format.