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Hidden Invariances in Problems of Two-Dimensional and Three-Dimensional Wall Jets for Newtonian and Non-Newtonian Fluids

This work is devoted to the investigation of self-similar solutions for steady wall jets. The problem is considered in the context of two- and three-dimensional Prandtl boundary layer equations, and three-dimensional parabolized Navier--Stokes equations for Newtonian and non-Newtonian fluids. In contrast to dimensional analysis, which does not allow the determination of self-similar solutions in this case, a generating functions approach elaborated by Vinogradov [Soviet Math. Dokl., 19 (1978), pp. 144--148] enables one to derive conservation laws for the above-mentioned problems and, as a consequence, to find new self-similarities of the Navier--Stokes equations.