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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:384

Article

Shirikyan, Armen

关键词: Complex Ginzburg-Landau equation;    Stationary measures;    Inviscid limit;    Local time;   

DOI  :  10.1016/j.jmaa.2010.12.043

来源: Elsevier

【 摘 要 】

We consider the behaviour of the distribution for stationary solutions of the complex Ginzburg-Landau equation perturbed by a random force. It was proved in S. Kuksin and A. Shirikyan (2004) [4] that if the random force is proportional to the square root of the viscosity v > 0, then the family of stationary measures possesses an accumulation point as v --> 0(+). We show that if mu is such a 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 Ito's formula and some properties of local time for semimartingales. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

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