Exponential attractors and their relevance to fluid dynamics systems
This paper investigates the theory of exponential attractors and its significance in infinite dimensional dynamical systems. The authors study a general class of parabolic P.D.E. with emphasis given to the 2D Navier- Stokes equations. Kuramoto-Sivashinsky equation is also studied briefly. In the study of the 2D incompressible Navier-Stokes equations with periodic boundary conditions on a box, an exponential attractor is obtained by adding a select number of points to the global attractor. The fact it is an exponential attractor follows from an a priori bound and exponential convergence of energy. This exponential attractor in the enstrophy space has same dimension and 1/2 the order of convergence than in the energy space.
scientific article; zbMATH DE number 221889