Similarity solutions of the Euler equation and the Navier-Stokes equation in two space dimensions
type: Item
instance of: scholarly article
title: Similarity solutions of the Euler equation and the Navier-Stokes equation in two space dimensions
zbMATH Open document ID: 0576.35005
DOI: 10.1007/BF00669790
published in: International Journal of Theoretical Physics
publication date: 1985-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 35A30
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 35L60
Mathematics Subject Classification ID: 35A25
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 47D03
zbMATH DE Number: 3921038
zbMATH Keywords: group theoretic method
zbMATH Keywords: Lie algebra
zbMATH Keywords: infinitesimal generators
zbMATH Keywords: one- parameter symmetry groups
zbMATH Keywords: Euler equations
zbMATH Keywords: Navier-Stokes equations
zbMATH Keywords: similarity variable
zbMATH Keywords: similarity solutions
author: Adolf Grauel
author: Willi-Hans Steeb
MaRDI profile type: Publication
cites work: Similarity methods for differential equations
cites work: Similarity transformations for the two-dimensional, unsteady, stream-function equation
cites work: The infinitesimal group of the Navier-Stokes equations
cites work: A nonlinear Hamiltonian structure for the Euler equations
cites work: Invariant group solutions of hydrodynamical equations
full work available at URL: https://doi.org/10.1007/bf00669790
OpenAlex ID: W2090120234
description: scientific article; zbMATH DE number 3921038