Exponential attractors and their relevance to fluid dynamics systems
type: Item
instance of: scholarly article
title: Exponential attractors and their relevance to fluid dynamics systems
zbMATH Open document ID: 0790.34053
DOI: 10.1016/0167-2789(93)90116-I
published in: Physica D
publication date: 1993-06-29T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 34D45
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 37-XX
zbMATH DE Number: 221889
zbMATH Keywords: exponential attractors
zbMATH Keywords: infinite dimensional dynamical systems
zbMATH Keywords: parabolic P.D.E.
zbMATH Keywords: 2D Navier-Stokes equations
zbMATH Keywords: Kuramoto-Sivashinsky equation
zbMATH Keywords: enstrophy space
author: A. Eden
author: Ciprian Foias
author: Basil Nicolaenko
author: Zhen-Su She
reviewed by: Joseph G. G. Yan
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 221889