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

Armen Shirikyan (1)

1 AGM - UMR 8088 - Analyse, Géométrie et Modélisation

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 µ is such point, then the distributions of the L² 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.

Mots clés: complex Ginzburg-Landau equation; stationary measures; inviscid limit; local time

Domaines: Equations aux dérivées partielles [math.AP]; Probabilités [math.PR]

Armen Shirikyan. Local times for solutions of the complex Ginzburg-Landau equation and the inviscid limit. 2010. ⟨hal-00461510⟩