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On the Bardina’s Model in the Whole Space

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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 \(t \in [0, \infty [\).

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Acknowledgements

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

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Authors and Affiliations

  1. Fluminance Team, INRIA, IRMAR, UMR 6625, Université Rennes 1, Campus Beaulieu, 35042, Rennes Cedex, France

    Roger Lewandowski

  2. Dipartimento di Matematica, Università di Pisa, Via F. Buonarroti 1/c, 56127, Pisa, Italy

    Luigi C. Berselli

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  1. Roger Lewandowski
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  2. Luigi C. Berselli
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Correspondence to Roger Lewandowski.

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Communicated by G.P. Galdi

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Lewandowski, R., Berselli, L.C. On the Bardina’s Model in the Whole Space. J. Math. Fluid Mech. 20, 1335–1351 (2018). https://doi.org/10.1007/s00021-018-0369-2

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