Pullback exponential attractor of dynamical systems associated with non-cylindrical problems

Abstract

In this work, we present a way of approaching the theory of pullback exponential attractors for dynamical systems on time-dependent phase spaces (or dynamical systems associated with non-cylindrical problems). We will show that these types of dynamical systems satisfying the smoothing property have a pullback exponential attractor, extending the results for dynamical systems defined on a fixed phase space, e.g. [5], [15], [25]. Furthermore, we will apply this theory to show that the dynamical system associated with the 2D-Navier-Stokes equations on some non-cylindrical domain has a pullback exponential attractor on a suitable tempered universe that depends on the time integrability of the external force and the behavior of the initial conditions.