SINOPSIS

Various forms of scale-invariant variables, functions and differential equations, including the generalized Blasius equation, are obtained on a basis of Lie groups. It is shown that form of the general ordinary differential equation is determined by choice of a parametric variable. Using symmetry properties, the generalized Blasius equation is reduced to a first order equation. Two new scale-invariant solutions of the Prandtl equations are obtained. A way of transforming the one-parameter Lie algebra of the Prandtl equations, involving four subalgebras, to an algebra with three subalgebras, one of which is two-parameter subalgebra, is shown.