Abstract:
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.
Bibliography: 11 titles.
Citation:
A. V. Fursikov, “On uniqueness of the solution of the chain of moment equations corresponding to the three-dimensional Navier–Stokes system”, Math. USSR-Sb., 62:2 (1989), 465–490
\Bibitem{Fur87}
\by A.~V.~Fursikov
\paper On~uniqueness of the~solution of the~chain of~moment equations corresponding to the three-dimensional Navier--Stokes system
\jour Math. USSR-Sb.
\yr 1989
\vol 62
\issue 2
\pages 465--490
\mathnet{http://mi.mathnet.ru/eng/sm2502}
\crossref{https://doi.org/10.1070/SM1989v062n02ABEH003249}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=933698}
\zmath{https://zbmath.org/?q=an:0665.76035}
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https://www.mathnet.ru/eng/sm2502
https://doi.org/10.1070/SM1989v062n02ABEH003249
https://www.mathnet.ru/eng/sm/v176/i4/p472
This publication is cited in the following 4 articles:
A. V. Fursikov, Fundamental Problematic Issues in Turbulence, 1999, 17
A. V. Fursikov, O. Yu. Imanuvilov, “The rate of convergence of approximations for the closure of the Friedman–Keller chain in the case of large Reynolds numbers”, Russian Acad. Sci. Sb. Math., 81:1 (1995), 235–259
A. V. Fursikov, “Moment theory for the Navier–Stokes equations with a random right side”, Russian Acad. Sci. Izv. Math., 41:3 (1993), 515–555
A. V. Fursikov, Lecture Notes in Mathematics, 1530, The Navier-Stokes Equations II — Theory and Numerical Methods, 1992, 226
Citation in format AMSBIB
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