Geodesic
Unsteady 2D motions a viscous fluid described by partially invariant solutions to the Navier--Stokes equations
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 8 (2015) no. 2, pp. 140-147

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3D continuous subalgebra is used to searching partially invariant solution of viscous incompressible fluid equations. It can be interpreted as a 2D motion of one or two immiscible fluids in plane channel. The arising initial boundary value problem for factor-system is an inverse one. Unsteady problem for creeping motions is solved by separating of variables method for one fluid or Laplace transformation method for two fluids.
Keywords: partially invariant solution, free boundary problem
Mots-clés : viscous fluid, interface. 
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     title = {Unsteady {2D} motions a viscous fluid described by partially invariant solutions to the {Navier--Stokes} equations},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
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Victor K. Andreev. Unsteady 2D motions a viscous fluid described by partially invariant solutions to the Navier--Stokes equations. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 8 (2015) no. 2, pp. 140-147. http://geodesic.mathdoc.fr/item/JSFU_2015_8_2_a2/