Similarity solutions of the Euler equation and the Navier-Stokes equation in two space dimensions

DOI10.1007/BF00669790zbMath0576.35005OpenAlexW2090120234MaRDI QIDQ1065245

Willi-Hans Steeb, Adolf Grauel

Publication date: 1985

Published in: International Journal of Theoretical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00669790

zbMATH Keywords

Navier-Stokes equationsEuler equationsLie algebragroup theoretic methodsimilarity solutionsinfinitesimal generatorssimilarity variableone- parameter symmetry groups

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Navier-Stokes equations (35Q30) First-order nonlinear hyperbolic equations (35L60) Groups and semigroups of linear operators (47D03) Geometric theory, characteristics, transformations in context of PDEs (35A30) Other special methods applied to PDEs (35A25)

Related Items (8)

Bogus transformations in mechanics of continua ⋮ Similarity analysis of modified shallow water equations and evolution of weak waves ⋮ Lie-symmetry vector fields for linear and nonlinear wave equations ⋮ Similarity solutions for three-dimensional Euler equations using Lie group analysis ⋮ One class of regular partially invariant solutions of the Navier-Stokes equations ⋮ On some new exact solutions of incompressible steady state Navier-Stokes equations ⋮ Vortices and invariant surfaces generated by symmetries for the 3D Navier-Stokes equations ⋮ Exact solutions to magnetogasdynamic equations in Lagrangian coordinates

Cites Work

• A nonlinear Hamiltonian structure for the Euler equations
• The infinitesimal group of the Navier-Stokes equations
• Invariant group solutions of hydrodynamical equations
• Similarity methods for differential equations
• Similarity transformations for the two-dimensional, unsteady, stream-function equation

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