Abstract
The work is a survey of the author’s results with modifications and preliminary information on the use of stochastic analysis on Sobolev groups of diffeomorphisms of a flat n-dimensional torus to describe the motion of viscous fluids (nonrandom ones). The main idea is to replace the covariant derivatives on the groups of diffeomorphisms in the equations introduced by Ebin and Marsden to describe ideal fluids by the so-called mean derivatives of random processes.
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Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 67, No. 2, Dedicated to the memory of Professor N. D. Kopachevsky, 2021.
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Gliklikh, Y. Stochastic Lagrange Approach to Viscous Hydrodynamics. J Math Sci 278, 82–90 (2024). https://doi.org/10.1007/s10958-024-06906-7
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DOI: https://doi.org/10.1007/s10958-024-06906-7