Geodesic
Group analysis of equations of hydrostatic model of viscous fluid
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 3, pp. 342-350.

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The group properties of three-dimensional equations of hydrostatic model of viscous fluid are studied. Several exact solutions are presented. The free surface of fluid and pressure on this surface are determined.
Keywords: hydrostatic model, group analysis
Mots-clés : viscous fluid, exact solution. 
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Alexander A. Rodionov; Daria A. Krasnova. Group analysis of equations of hydrostatic model of viscous fluid. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 3, pp. 342-350. http://geodesic.mathdoc.fr/item/JSFU_2019_12_3_a8/

[1] L.V. Ovsjannikov, Group Properties of Differential Equations, English translation by G. W. Bluman, USSR Academy of Science, Siberian Section, Novosibirsk, 1962 | MR

[2] L.V. Ovsjannikov, Group Analysis of Differential Equations, English translation by W. F. Ames, Academic, New York, 1982 | MR

[3] N.H. Ibragimov, Transformation Group in Mathematical Physics, Transformation Groups Applied to Mathematical Physics, Reidel, Dordrecht, 1985 | DOI | MR

[4] V.K. Andreev, O.V. Kaptsov, V.V. Pukhnachev, A.A. Rodionov, Applications of Group-Theoretical Methods in Hydrodynamics, Kluwer Academic Publishers, U.S.A, 1998 (in Russian) | MR | Zbl

[5] K.F. Bowden, Physical Oceanography of Coastal Waters, Ellis Horwood Limited Publishers, New York; Halsted Press, 1983

[6] A.A. Rodionov, “Hydrostatic Model for an Ideal Fluid: Group Properties of Equations and their Solutions”, Journal of Siberian Federal University. Mathematics and Physics, 8:3 (2015), 320–326 (in Russian) | DOI | MR

[7] V.O. Bytev, “Group properties of the Navier-Stokes equations”, Numerical methods of continuum mechanics, 3:3 (1972), 13–17 (in Russian) | MR

[8] A.D. Polyanin, Reference book. Linear Equations of mathematical physics, Nauka, M., 1983 (in Russian) | MR