On the common exact solutions of stationary Navier-Stokes and quasi-hydrodynamic systems, not satisfying to Euler equations
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 2 (2017), pp. 5-15 Cet article a éte moissonné depuis la source Math-Net.Ru

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Three families of exact solutions, which are common for the stationary Navier-Stokes system and corresponding quasi-hydrodynamic system, are constructed. These solutions do not satisfy to Euler equations. The concrete examples of solutions that describe the flows of a viscous fluid are presented. Their physical interpretation is given.
Keywords: Navier-Stokes and Euler systems
Mots-clés : quasi-hydrodynamic equations, exact solutions.
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Yu. V. Sheretov. On the common exact solutions of stationary Navier-Stokes and quasi-hydrodynamic systems, not satisfying to Euler equations. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 2 (2017), pp. 5-15. http://geodesic.mathdoc.fr/item/VTPMK_2017_2_a0/

[1] Landau L. D., Lifshits E. M., Hydrodynamics, “Nauka” Publ., Moscow, 1986, 736 pp. (in Russian) | MR

[2] Loytsyansky L. G., Fluid and Gas Mechanics, “Nauka” Publ., Moscow, 1987, 840 pp. (in Russian) | MR

[3] Sheretov Yu. V., “On uniqueness of the solutions for one dissipative system of hydrodynamic type”, Mathematical Modeling, 6:10 (1994), 35-45 (in Russian) | MR | Zbl

[4] Sheretov Yu. V., Continuum Dynamics under Spatiotemporal Averaging, “Regular and Chaotic Dynamics” Publ., Moscow, Izhevsk, 2009, 400 pp. (in Russian)

[5] Sheretov Yu. V., Regularized Hydrodynamic Equations, Tver State University, Tver, 2016, 222 pp. (in Russian)

[6] Sheretov Yu. V., “On the exact solutions of stationary quasi-hydrodynamic equations in cylindrical coordinates”, Vestnik TvGU. Seriya: Prikladnaya matematika [Herald of Tver State University. Series: Applied Mathematics], 2017, no. 1, 85-94 (in Russian)

[7] Zherikov A. V., Application of Quasi-Hydrodynamic Equations: Mathematical Modeling of Viscous Incompressible Fluid, Lambert Academic Publishing, Saarbrücken, 2010, 124 pp. (in Russian)

[8] Elizarova T. G., Milyukova O. Yu., “Numerical simulation of viscous incompressible flow in a cubic cavity”, Computational Mathematics and Mathematical Physics, 43:3 (2003), 453-466 (in Russian) | MR | Zbl