Necessary and sufficient conditions for the existence of exponential attractors for semigroups, and applications

First we establish some necessary and sufficient conditions for the existence of exponential attractors by using ωω-limit compactness and a measure of non-compactness. Then we provide a new method for proving the existence of exponential attractors. We prove the existence of exponential attractors for reaction–diffusion equations and 2D Navier–Stokes equations as simple applications.