Exponential Attractors in Hilbert and Banach Spaces

Bong-Sik Kim

Published 2020-02-27Version 1

Exponential attractors describe the long-time behavior of dissipative dynamical systems. In this note, we dwell on the notions of exponential attractors for strongly continuous semigroups acting on complete metric spaces. We address the construction of the exponential attractors in two different functional space settings; one in Hilbert space, the other in Banach space. The former relies on the squeezing properties of solution trajectories, and the latter does not. We present these different approaches for the construction of exponential attractors with the three-dimensional Lagrangian-averaged Navier-Stokes system. Then, we compare those attractors obtained from two different methods and show their difference.