Multivalued Attractors and their Approximation: Applications to the Navier-Stokes equations
Numerical Analysis
2012-02-09 v2
Abstract
This article is devoted to the study of multivalued semigroups and their asymptotic behavior, with particular attention to iterations of set-valued mappings. After developing a general abstract framework, we present an application to a time discretization of the two-dimensional Navier-Stokes equations. More precisely, we prove that the fully implicit Euler scheme generates a family of discrete multivalued dynamical systems, whose global attractors converge to the global attractor of the continuous system as the time-step parameter approaches zero.
Keywords
Cite
@article{arxiv.1111.4368,
title = {Multivalued Attractors and their Approximation: Applications to the Navier-Stokes equations},
author = {Michele Coti Zelati and Florentina Tone},
journal= {arXiv preprint arXiv:1111.4368},
year = {2012}
}