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Space averages and homogeneous fluid flows. (English) Zbl 1064.76057

Summary: The relation between space averages of vector fields in \(L^1_{\text{loc}}(\mathbb R^3)\) and averages with respect to homogeneous measures on such vector fields is examined. The space average, obtained by integration over balls in space, is shown to exist almost always and, whenever the measure is ergodic or the correlation decays, the space average is to equal the ensemble average.

MSC:

76F05 Isotropic turbulence; homogeneous turbulence
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