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Multivalued attractors and their approximation: applications to the Navier–Stokes equations

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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.

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Authors and Affiliations

  1. Department of Mathematics, Indiana University, Rawles Hall, Bloomington, IN, 47405, USA

    Michele Coti Zelati

  2. Department of Mathematics and Statistics, University of West Florida, Pensacola, FL, 32514, USA

    Florentina Tone

Authors
  1. Michele Coti Zelati
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  2. Florentina Tone
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Correspondence to Michele Coti Zelati.

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Coti Zelati, M., Tone, F. Multivalued attractors and their approximation: applications to the Navier–Stokes equations. Numer. Math. 122, 421–441 (2012). https://doi.org/10.1007/s00211-012-0463-y

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  • DOI: https://doi.org/10.1007/s00211-012-0463-y

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