Geodesic
Research of equations of a viscous inhomogeneous fluid in a Hele--Shaw cell by group analysis method
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 17 (2024) no. 4, pp. 528-536.

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The main group of transformations allowed by the system of differential equations for the flow of a viscous inhomogeneous fluid in a Hele–Shaw cell is constructed in this paper. A classifying equation for the viscosity function is obtained. A basis of operators that preserve the form of the original equations is constructed. The basis of the space of solutions of defining equations is described. Invariants of operators are found and invariant solutions of the equations are obtained.
Keywords: group analysis, infinitesimal operator, Hele–Shaw cell.
Mots-clés : fluid equations, invariant, invariant solution 
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Alexander A. Rodionov; Nikita A. Saveliev. Research of equations of a viscous inhomogeneous fluid in a Hele--Shaw cell by group analysis method. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 17 (2024) no. 4, pp. 528-536. http://geodesic.mathdoc.fr/item/JSFU_2024_17_4_a11/

[1] D.A.Krasnova, A.A.Rodionov, I.V.Stepanova, Continuous groups of equations, tutorial, Siberian Federal University, Krasnoyarsk, 2017

[2] L.V.Ovsiannikov, Group Analysis of Differential Equations, Nauka, M., 1978 | MR | Zbl

[3] A.Chesnokov, V.Liapidevskii, I.Stepanova, “Roll waves structure in two-layer Hele-Shaw flows”, Wave Motion, 73 (2017), 1–10 | DOI | MR | Zbl