Geodesic
Some results on the Navier-Stokes equations in connection with the statistical theory of stationary turbulence
Applications of Mathematics, Tome 47 (2002) no. 6, pp. 485-516.

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Some rigorous results connected with the conventional statistical theory of turbulence in both the two- and three-dimensional cases are discussed. Such results are based on the concept of stationary statistical solution, related to the notion of ensemble average for turbulence in statistical equilibrium, and concern, in particular, the mean kinetic energy and enstrophy fluxes and their corresponding cascades. Some of the results are developed here in the case of nonsmooth boundaries and a less regular forcing term and for arbitrary stationary statistical solutions.
DOI : 10.1023/A:1023297721804
Classification : 35Q30, 37L40, 76D05, 76D06, 76F05, 76F20
Keywords: Navier-Stokes equations; statistical solutions; turbulence; energy cascade; enstrophy cascade 
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Rosa, Ricardo M. S. Some results on the Navier-Stokes equations in connection with the statistical theory of stationary turbulence. Applications of Mathematics, Tome 47 (2002) no. 6, pp. 485-516. doi : 10.1023/A:1023297721804. http://geodesic.mathdoc.fr/articles/10.1023/A:1023297721804/

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