Local times for solutions of the complex Ginzburg-Landau equation and the inviscid limit

We consider the behaviour of the distribution for stationary solutions of the complex Ginzburg-Landau equation perturbed by a random force. It was proved earlier that if the random force is proportional to the square root of the viscosity, then the family of stationary measures possesses an accumula...

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Bibliographic Details
Published inarXiv.org
Main Author Shirikyan, Armen
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 04.03.2010
Subjects
Landau-Ginzburg equations
Viscosity
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Summary:We consider the behaviour of the distribution for stationary solutions of the complex Ginzburg-Landau equation perturbed by a random force. It was proved earlier that if the random force is proportional to the square root of the viscosity, then the family of stationary measures possesses an accumulation point as the viscosity goes to zero. We show that if \(\mu\) is such point, then the distributions of the L^2 norm and of the energy possess a density with respect to the Lebesgue measure. The proofs are based on Itô's formula and some properties of local time for semimartingales.
ISSN:2331-8422