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arXiv · 1205.5563

On the convergence of statistical solutions of the 3D Navier-Stokes-$\alpha$ model as $\alpha$ vanishes

Anne C. Bronzi·Ricardo M. S. Rosa
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Abstract

In this paper statistical solutions of the 3D Navier-Stokes-$\alpha$ model with periodic boundary condition are considered. It is proved that under certain natural conditions statistical solutions of the 3D Navier-Stokes-$\alpha$ model converge to statistical solutions of the exact 3D Navier-Stokes equations as $\alpha$ goes to zero. The statistical solutions considered here arise as families of time-projections of measures in suitable trajectory spaces.

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Anne C. Bronzi, Ricardo M. S. Rosa. 2012-05-24. On the convergence of statistical solutions of the 3D Navier-Stokes-$\alpha$ model as $\alpha$ vanishes. https://doi.org/10.3934/dcds.2014.34.19

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