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Journal of Mathematical Fluid Mechanics

, Volume 20, Issue 3, pp 1335–1351 | Cite as

On the Bardina’s Model in the Whole Space

  • Roger Lewandowski
  • Luigi C. Berselli
Article

Abstract

We consider the Bardina’s model for turbulent incompressible flows in the whole space with a cut-off frequency of order \(\alpha ^{-1} >0\). We show that for any \(\alpha >0\) fixed, the model has a unique regular solution defined for all \(t \in [0, \infty [\).

Keywords

Navier–Stokes equations Bardina’s model Regular solutions Helmholtz filter 

Mathematics Subject Classification

35Q30 35D30 76D03 76D05 

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Notes

Acknowledgements

The research that led to the present paper was partially supported by a grant of the group GNAMPA of INdAM.

Compliance with ethical standards

Conflicts of interest

The authors declare that they have no conflict of interest.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Fluminance Team, INRIA, IRMAR, UMR 6625Université Rennes 1Rennes CedexFrance
  2. 2.Dipartimento di MatematicaUniversità di PisaPisaItaly

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