  We prove the existence of an Inertial Manifold for 3D complex Ginzburg-Landau
equation with periodic boundary conditions as well as for more general
cross-diffusion system assuming that the dispersive exponent is not vanishing.
The result is obtained under the assumption that the parameters of the equation
is chosen in such a way that the finite-time blow up of smooth solutions does
not take place. For the proof of this result we utilize the recently suggested
method of spatio-temporal averaging.
