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Solution of the system of Navier–Stokes equations linearized with respect to the velocity with regard of a power-law dependence of viscosity, thermal conductivity and the gaseous medium density on the temperature

Annotation

We received the solution of the system of Navier–Stokes equations linearized with respect to the velocity in the spheroidal coordinate system with regard of a power-law dependence of viscosity, thermal conductivity and the gaseous medium density on the temperature by means of generalized power series.

Keywords

system of Navier–Stokes equations; a spheroid

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DOI

10.20310/1810-0198-2018-23-123-448-455

UDC

517.958

Pages

448-455

References

1. Happel J., Brenner H. Gidrodinamika pri malykh chislakh Reynol’das [Low Reynolds Number Hydrodynamics]. Moscow, Mir Publ., 1960. (In Russian). 2. Koterov V.N., Shmyglevskiy Yu.D., Shcheprov A.V. Obzor analiticheskikh issledovaniy ustanovivshikhsya techeniy vyazkoy neszhimaemoy zhidkosti (2000-2004 gg.) [A survey of analytical studies of steady viscous incompressible flows (2000-2004)]. Zhurnal vychislitel’noy matematiki i matematicheskoy fiziki – Computational Mathematics and Mathematical Physics, 2005, vol. 45, no. 5, pp. 899-920. (In Russian). 3. Ladyzhenskaya O.A. Shestaya problema tysyacheletiya: uravneniya Nav’e–Stoksa. Sushchestvovanie i gladkost’ [Sixth problem of the millennium: Navier–Stokes equations, existence and smoothness]. Uspekhi matematicheskikh nauk – Russian Mathematical Surveys, 2003, vol. 58, no. 2 (350), pp. 45-78. (In Russian). 4. Malay N.V., Mironova N.N., Glushak A.V. Reshenie kraevoy zadachi dlya uravneniya Nav’e–Stoksa pri obtekanii nagretogo sferoida gazoobraznoy sredoy [Solution of the boundary value problem for the Navier–Stokes equation for the flow of a gaseous medium past a heated spheroid]. Differentsial’nye uravneniya – Differential Equations, 2012, vol. 48, no. 6, pp. 879-883. (In Russian). 5. Koddington E.A., Levinson N. Teoriya obyknovennykh differentsial’nykh uravneniy [Theory of Ordinary Differential Equations]. Moscow, Foreign Languages Publishing House, 1958. (In Russian). 6. Kamke E. Spravochnik po obyknovennym differentsial’nym uravneniyam [Typical Differential Equations Guide]. Moscow, State Publ. of Technical and Theoretical Literature, 1981, 703 p. (In Russian).

Received

2018-04-17

Section of issue

Scientific articles

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