Abstract
In this note we consider a family of statistical solutions of the Navier-Stokes equations (i.e. time dependent solutions of the Hopf equation) which seem to constitute the rigorous mathematical framework for the theory of homogeneous turbulence [1], [13]. The main feature of these solutions is that they are the transforms under suitable scalings of thestationary statistical solutions of a new system of equations (the Eq. (2) below).
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Foias, C., Temam, R. Self-similar universal homogeneous statistical solutions of the Navier-Stokes equations. Commun.Math. Phys. 90, 187–206 (1983). https://doi.org/10.1007/BF01205502
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DOI: https://doi.org/10.1007/BF01205502