Randomly forced CGL equation: Stationary measures and the inviscid limit

Sergei Kuksin, Armen Shirikyan

Research output: Contribution to journalArticle

Abstract

We study a complex Ginzburg-Landau (CGL) equation perturbed by a random force which is white in time and smooth in the space variable x. Assuming that dim = 4, we prove that this equation has a unique solution and discuss its asymptotic in time properties. Next we consider the case when the random force is proportional to the square root of the viscosity and study the behaviour of stationary solutions as the viscosity goes to zero. We show that, under this limit, a subsequence of solutions in question converges to a nontrivial stationary process formed by global strong solutions of the nonlinear Schrödinger equation.

Original languageEnglish
Pages (from-to)3805-3822
Number of pages18
JournalJournal of Physics A: Mathematical and General
Volume37
Issue number12
DOIs
Publication statusPublished - 26 Mar 2004

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Inviscid Limit
Stationary Measure
Complex Ginzburg-Landau Equation
Viscosity
Strong Solution
Stationary Process
Stationary Solutions
Subsequence
Square root
Unique Solution
Nonlinear Equations
Directly proportional
Converge
Zero

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Kuksin, Sergei ; Shirikyan, Armen. / Randomly forced CGL equation : Stationary measures and the inviscid limit. In: Journal of Physics A: Mathematical and General. 2004 ; Vol. 37, No. 12. pp. 3805-3822.
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Randomly forced CGL equation : Stationary measures and the inviscid limit. / Kuksin, Sergei; Shirikyan, Armen.

In: Journal of Physics A: Mathematical and General, Vol. 37, No. 12, 26.03.2004, p. 3805-3822.

Research output: Contribution to journalArticle

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