ВЕСТНИК ВГУ, Серия физика, математика, 2001, ¹ 1 UDK 519.216; 514.8 VISCOUS HYDRODYNAMICS THROUGH STOCHASTIC PERTURBATIONS OF FLOWS OF PERFECT FLUIDS ON GROUPS OF DIFFEOMORPHISMS* © 2001 г. <...> E. Gliklikh Voronezh State University We construct some stochastic perturbations of the curves on groups of Hs (s > 1 equations for s > 1 2 n +2 is proved (for s > 1 diffeomorphisms of a flat n-dimensional torus, describing the motion of diffuse matter or perfect incompressible fluid, such that their expectations describe the dynamics of corresponding viscous fluids. <...> Existence of classical solutions for initial value problem of Burgers and Navier-Stokes 2 n +1 of some sort of generalized solutions). 2 n +1) Sobolev The research is partially supported by Grant 99-01-00819 from RFBR and Grant 99-00559 from INTAS 83 84 Yu. <...> E. Gliklikh ВЕСТНИК ВГУ, Серия физика, математика, 2001, ¹ 1 Viscous hydrodynamics through stochastic perturbations of flows of perfect fluids on . 85 ВЕСТНИК ВГУ, Серия физика, математика, 2001, ¹ 1 86 Yu. <...> E. Gliklikh ВЕСТНИК ВГУ, Серия физика, математика, 2001, ¹ 1 Viscous hydrodynamics through stochastic perturbations of flows of perfect fluids on . 87 ВЕСТНИК ВГУ, Серия физика, математика, 2001, ¹ 1 88 Yu. <...> E. Gliklikh ВЕСТНИК ВГУ, Серия физика, математика, 2001, ¹ 1 Viscous hydrodynamics through stochastic perturbations of flows of perfect fluids on . 89 ВЕСТНИК ВГУ, Серия физика, математика, 2001, ¹ 1 90 Yu. <...> Arnol'd V. Sur la gйomйtrie diffйrentielle des groupes de Lie de dimension infinie et ses applications a l'hydrodynamique des fluides parfaits.// Ann. <...> I. Probabilistic representation of solutions to boundary value problems for hydrodynamic equations.// Proceedings of POMI, 1997 249, 71102. 3. <...> E. Diffusion processes on groups of diffeomorphisms and hydrodynamics of incompressible fluid.// Transactions of RANS, ser. MMMIC, 1999 Т. 3, N 2. <...> E. Stochastic processes on groups of diffeomorphisms and description of viscous hydrodynamics. <...> E. Lagrangian approach to hydrodynamics of viscous incompressible fluid.// Russian Math. <...> E. Stochastic analysis, groups of diffeomorphisms and Lagrangian <...>