- 01-403 Stamatis Dostoglou
- Homogeneous measures and spatial ergodicity of the Navier-Stokes
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.