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The Three-Dimensional Globally Modified Navier–Stokes Equations: Recent Developments

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Recent Trends in Dynamical Systems

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 35))

Abstract

The globally modified Navier–Stokes equations (GMNSE) were introduced by Caraballo, Kloeden and Real (Adv. Nonlinear Stud. 6:411–436, 2006) in 2006 and have been investigated in a number of papers since then, both for their own sake and as a means of obtaining results about the three-dimensional Navier–Stokes equations. These results were reviewed by Kloeden et al. (Advances in Nonlinear Analysis: Theory, Methods and Applications, Cambridge Scientific Publishers, Cambridge, 2009; pp 11–22.), which was published in 2009, but there have been some important developments since then, which will be reviewed here.

Herrn Prof. Dr. Jürgen Scheurle zu seinem sechzigsten Geburtstag gewidmet

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Acknowledgments

This work was partially supported by the Spanish Ministerio de Ciencia e Innovación project MTM2011-22411, the Consejería de Innovación, Ciencia y Empresa (Junta de Andalucía) under the Ayuda 2009/FQM314 and the Proyecto de Excelencia P07-FQM-02468.

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Authors and Affiliations

  1. Dpto. Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, ES-41080, Sevilla, Spain

    T. Caraballo

  2. Institut für Mathematik, Goethe-Universität, D-60054, Frankfurt am Main, Germany

    P. E. Kloeden

Authors
  1. T. Caraballo
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  2. P. E. Kloeden
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Corresponding author

Correspondence to P. E. Kloeden .

Editor information

Editors and Affiliations

  1. Zentrum Mathematik, Technische Universität München, Garching bei München, Germany

    Andreas Johann

  2. Zentrum Mathematik, Technische Universität München, Garching bei München, Germany

    Hans-Peter Kruse

  3. Zentrum Mathematik, Technische Universität München, Garching bei München, Germany

    Florian Rupp

  4. Zentrum Mathematik, Technische Universität München, Garching bei München, Germany

    Stephan Schmitz

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Caraballo, T., Kloeden, P.E. (2013). The Three-Dimensional Globally Modified Navier–Stokes Equations: Recent Developments. In: Johann, A., Kruse, HP., Rupp, F., Schmitz, S. (eds) Recent Trends in Dynamical Systems. Springer Proceedings in Mathematics & Statistics, vol 35. Springer, Basel. https://doi.org/10.1007/978-3-0348-0451-6_18

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