Sergei Kuksin, Armen Shirikyan
Randomly forced CGL equation: stationary measures and the inviscid limit
(200K, Postscript)

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 $\dim x\le4$, 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 Schr\"odinger equation.