01-403 Stamatis Dostoglou

Homogeneous measures and spatial ergodicity of the Navier-Stokes equations (192K, Postscript) Oct 30, 01

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Abstract. We show that the Vishik-Fursikov homogeneous statistical solutions of the Navier-Stokes equations extending homogeneous measures on initial conditions yield measures ergodic with respect to space translations if the initial measure is ergodic. Therefore, with respect to such a measure, space averages of almost any realization of the flow at any given time equal probability averages at any point in space at that time. Ergodic measures on the initial conditions exist.

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