English

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}
}