Lie groups and self-similar forms of the Prandtl equations (Q2755225)

On the basis of Lie groups various forms of self-similar variables, functions and differential equations are presented including the generalized Blasius equation. It is shown that the form of the corresponding system of ordinary differential equations is determined using the parametric variable. Starting from symmetry properties, the generalized Blasius equation is reduced to a system of first-order ordinary differential equations. Two new self-similar solutions of the Prandtl equations are obtained. The way is indicated to transform the one-parametric Lie algebra of Prandtl equations, containing four subalgebras, to the Prandtl algebra with three subalgebras, so that one of them is a two-parametric subalgebra.