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We consider the behaviour of the distribution for stationary solutions of thecomplex Ginzburg-Landau equation perturbed by a random force. It was provedearlier that if the random force is proportional to the square root of theviscosity, then the family of stationary measures possesses an accumulationpoint as the viscosity goes to zero. We show that if $\mu$ is such point, thenthe distributions of the L^2 norm and of the energy possess a density withrespect to the Lebesgue measure. The proofs are based on It\^o's formula andsome properties of local time for semimartingales.

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