On uniqueness of the solution of the chain of moment equations corresponding to the three-dimensional Navier–Stokes system

A theorem is proved on the uniqueness of the solution of the Cauchy problem for the chain of equations for the spatial moments corresponding to smooth solutions of the three-dimensional Navier–Stokes system in the case of any Reynolds numbers. By means of the uniqueness theorem it is proved that any solution of the chain of moment equations belonging to an appropriate function space forms a positive-definite system of moments for any time $t>0$ if its initial value was positive definite.
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