FINITE DIMENSIONALITY OF ATTRACTORS FOR NON-AUTONOMOUS DYNAMICAL SYSTEMS GIVEN BY PARTIAL DIFFERENTIAL EQUATIONS
In the last decade, the concept of pullback attractor has become one of the usual tools to describe some qualitative properties of non-autonomous partial differential equations. A pullback attractor is a family of compact sets, invariant for the corresponding process related to the equation, and attracting from the past, and it assumes a natural generalization of the now classical concept of global attractor for autonomous partial differential equations. In this work we give sufficient conditions in order to prove the finite Hausdorff and fractal dimensionality of pullback attractors for non-autonomous infinite dimensional dynamical systems, and we apply our results to a generalized non-autonomous partial differential equation of Navier–Stokes type.