Abstract
Solutions of nonstationary Euler equations on a torus in R3 are investigated. For a broad class of random initial velocity fields a measure in L2(Ω× [0, T]) is constructed, the moments of which for any finite T are solutions of the corresponding chain of moment equations.
Similar content being viewed by others
References
M. I. Vishik and A. I. Komech, “Statistical solutions of the Navier-Stokes and Euler equations,” Uspekhi Mekh.,5, No. 1–2, 65–120 (1982).
M. J. Vishik and A. V. Fursikov, Mathematical Problems of Statistical Hydrodynamics, Kluwer, Dordrecht (1988).
N. Dunford and J. T. Schwartz, Linear Operators, Part I: General Theory, Interscience, New York (1958).
R. J. DiPerna and A. J. Majda, “Oscillations and concentrations in weak solutions of the incompressible fluid equations,” Comm. Math. Phys.,108, No. 4, 667–689 (1987).
Additional information
Translated from Problemy Matematicheskogo Analiza, No. 11, pp. 27–37, 1990.
Rights and permissions
About this article
Cite this article
Maslova, N.B. Statistical solutions of Euler's equations. J Math Sci 64, 1240–1247 (1993). https://doi.org/10.1007/BF01098016
Issue Date:
DOI: https://doi.org/10.1007/BF01098016