Abstract
We study metric properties of trajectory attractors for infinite-dimensional dissipative systems. Under natural conditions we show that in the appropriate topology the functional dimension of this attractor is not greater than 1 and the metric order is 0. We also prove that every finite (in time) “piece” of the trajectory attractor has finite fractal dimension. As examples we consider a reaction-diffusion system, the 2D Navier-Stokes equation and also 3D Navier-Stokes equation under an additional regularity assumption concerning the corresponding trajectory attractor which is valid in the case of thin domains
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