Similarity solutions of the Euler equation and the Navier-Stokes equation in two space dimensions
Using the now familiar group theoretic method, the authors start with the already known infinite dimensional Lie algebra of infinitesimal generators of one-parameter symmetry groups for the Euler equations and the Navier-Stokes equations in two space dimensions. From this Lie algebra, they select in several different ways a two-dimensional Lie- subalgebra, and the usual procedure involving a similarity variable [see e.g. \textit{G. W. Bluman} and \textit{J. D. Cole}, ''Similarity methods for differential equations'' (1974; Zbl 0292.35001)] then leads to a system of ordinary differential equations. The corresponding similarity solutions are not discussed.
scientific article; zbMATH DE number 3921038