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An estimate for the mean square of the difference of velocities for homogeneous statistical solutions of the three-dimensional Navier-Stokes system

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Abstract

Stationary (with respect to t) statistical solutions of the Navier-Stokes system are constructed, in the presence of random external forces which are (statistically) stationary with respect to t. The domains considered are invariant under certain groups of motions (shifts and rotations). The external forces are supposed to be (statistically) invariant with respect to these groups and the constructed statistical solutions are also invariant in the same sense. For the constructed solutions, estimates of the mean square of the difference of velocities at different points are obtained in terms of a certain power of the distance between the points. The exponent depends on the dimension of the symmetry group.

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Literature cited

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Authors
  1. M. I. Vishik
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  2. A. I. Komech
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Additional information

Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 11, pp. 3–11, 1986.

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Vishik, M.I., Komech, A.I. An estimate for the mean square of the difference of velocities for homogeneous statistical solutions of the three-dimensional Navier-Stokes system. J Math Sci 45, 1367–1373 (1989). https://doi.org/10.1007/BF01097156

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  • DOI: https://doi.org/10.1007/BF01097156

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