Geodesic
The evolution of measures determined by the Navier--Stokes equations and on the solvability of the Cauchy problem for the Hopf statistical equation
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 9, Tome 59 (1976), pp. 3-24

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We prove the solvability of the Cauchy problem for Hopf's statistical equation, corresponding to the general three-dimensional initial- and boundary-value problem for the Navier–Stokes equations, with the assumption that the exterior forces and the boundary conditions are fixed while the initial field of the velocities is stochastic. Preliminarily we construct a family of measurable single-valued mappings $W_t$ defining the evolution $\mu_t$ of the probability measure $\mu$, given on the metric space $Y_R$ of the initial field of velocities according to the formula: $\mu_t(\omega)=\mu(W_t^{-1}\omega)$, where $\omega$ is any set from the $\sigma$-algebra $\Sigma(Y_R)$ of analytic sets of the space $Y_R$. 
@article{ZNSL_1976_59_a0,
     author = {A. M. Vershik and O. A. Ladyzhenskaya},
     title = {The evolution of measures determined by the {Navier--Stokes} equations and on the solvability of the {Cauchy} problem for the {Hopf} statistical equation},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {3--24},
     publisher = {mathdoc},
     volume = {59},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1976_59_a0/}
}
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A. M. Vershik; O. A. Ladyzhenskaya. The evolution of measures determined by the Navier--Stokes equations and on the solvability of the Cauchy problem for the Hopf statistical equation. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 9, Tome 59 (1976), pp. 3-24. http://geodesic.mathdoc.fr/item/ZNSL_1976_59_a0/