The complex Ginzburg-Landau equation on large and unbounded domains: Sharper bounds and attractors

Using weighted L(P)-norms we derive new bounds on the long-time behaviour of the solutions improving on the known results of the polynomial growth with respect to the instability parameter. These estimates are valid for quite arbitrary, possibly unbounded domains. We establish precise estimates on the maximal influence of the boundaries on the dynamics in the interior. For instance, the attractor Al for the domain (-l, l)(d) with periodic boundary conditions is upper semicontinuous to A(infinity).