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Decomposition and exact solutions of three-dimensional nonstationary linearized equations for a viscous fluid

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Abstract

A new exact method for solving three-dimensional linear systems of hydrodynamic equations is described based on decomposing these systems into three simpler equations. It is shown that the general solution to three-dimensional Stokes equations (when there are no mass forces) can be expressed by means of solutions to two independent equations: the heat conduction equation and the Laplace equation. A class of solutions with the linear dependence of velocity components on two space variables is studied, and their physical interpretation is given. Axial flows are considered, and certain hydrodynamic problems are solved. A general solution to three-dimensional Oseen equations is constructed. The linearized equations of motion for a viscoelastic Oldroyd fluid are studied

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Authors and Affiliations

  1. Ishlinskii Institute for Problems in Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101, Moscow, 119526, Russia

    A. D. Polyanin

  2. Environmental and Chemical Engineering Institute, Moscow State University of Mechanical Engineering, Staraya Basmannaya ul. 21/4, Moscow, 105066, Russia

    A. V. Vyazmin

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  1. A. D. Polyanin
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Correspondence to A. D. Polyanin.

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Original Russian Text © A.D. Polyanin, A.V. Vyazmin, 2013, published in Teoreticheskie Osnovy Khimicheskoi Tekhnologii, 2013, Vol. 47, No. 2, pp. 158–167.

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Polyanin, A.D., Vyazmin, A.V. Decomposition and exact solutions of three-dimensional nonstationary linearized equations for a viscous fluid. Theor Found Chem Eng 47, 114–123 (2013). https://doi.org/10.1134/S0040579513020061

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