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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.
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