Global attractor for the Navier–Stokes equations with fractional deconvolution

  • Davide Catania
  • Alessandro Morando
  • Paola Trebeschi


We consider a large eddy simulation model for the 3D Navier–Stokes equations obtained through fractional deconvolution of generic order. The global well-posedness of such a problem is already known. We prove the existence of the global attractor for the solution operator and find estimates for its Hausdorff and fractal dimensions both in terms of the Grashoff number and in terms of the mean dissipation length, with particular attention to the dependence on the fractional and deconvolution parameters. These results can be interpreted as bounds for the number of degrees of freedom of long-time dynamics, thus providing further information on the validity of the model for the simulation of turbulent 3D flows.


Navier–Stokes equations Global attractor Fractal and Hausdorff dimension Approximate deconvolution models (ADM) and methods Fractional filter Large eddy simulation (LES) 

Mathematics Subject Classification

76D05 35Q30 76F65 76D03 


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Copyright information

© Springer Basel 2014

Authors and Affiliations

  • Davide Catania
    • 1
    • 2
  • Alessandro Morando
    • 1
  • Paola Trebeschi
    • 1
  1. 1.DICATAM, Sezione MatematicaUniversità degli Studi di BresciaBresciaItaly
  2. 2.Facoltà di IngegneriaUniversità degli Studi eCampusNovedrateItaly

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