Symmetry-invariant conservation laws of partial differential equations

A simple characterization of the action of symmetries on conservation laws of partial differential equations is studied by using the general method of conservation law multipliers. This action is used to define symmetry-invariant and symmetry-homogeneous conservation laws. The main results are appli...

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Published inEuropean journal of applied mathematics Vol. 29; no. 1; pp. 78 - 117
Main Authors ANCO, STEPHEN C., KARA, ABDUL H.
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.02.2018
Subjects
Applied mathematics
Compressibility
Conservation laws
Fluid dynamics
Invariants
Mathematical analysis
Navier-Stokes equations
Partial differential equations
Symmetry
Viscous fluids
symmetry-invariant
multipliers
symmetry
conservation law
symmetry-homogeneous
Online AccessGet full text
ISSN0956-7925
1469-4425
DOI10.1017/S0956792517000055

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Abstract A simple characterization of the action of symmetries on conservation laws of partial differential equations is studied by using the general method of conservation law multipliers. This action is used to define symmetry-invariant and symmetry-homogeneous conservation laws. The main results are applied to several examples of physically interest, including the generalized Korteveg-de Vries equation, a non-Newtonian generalization of Burger's equation, the b-family of peakon equations, and the Navier–Stokes equations for compressible, viscous fluids in two dimensions.
AbstractList A simple characterization of the action of symmetries on conservation laws of partial differential equations is studied by using the general method of conservation law multipliers. This action is used to define symmetry-invariant and symmetry-homogeneous conservation laws. The main results are applied to several examples of physically interest, including the generalized Korteveg-de Vries equation, a non-Newtonian generalization of Burger's equation, the b -family of peakon equations, and the Navier–Stokes equations for compressible, viscous fluids in two dimensions.
A simple characterization of the action of symmetries on conservation laws of partial differential equations is studied by using the general method of conservation law multipliers. This action is used to define symmetry-invariant and symmetry-homogeneous conservation laws. The main results are applied to several examples of physically interest, including the generalized Korteveg-de Vries equation, a non-Newtonian generalization of Burger's equation, the b-family of peakon equations, and the Navier–Stokes equations for compressible, viscous fluids in two dimensions.
Author ANCO, STEPHEN C.
KARA, ABDUL H.
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  surname: KARA
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  organization: School of Mathematics, University of the Witwatersrand Wits 2050, Johannesburg, South Africa email: abdul.kara@wits.ac.za
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SubjectTerms Applied mathematics
Compressibility
Conservation laws
Fluid dynamics
Invariants
Mathematical analysis
Navier-Stokes equations
Partial differential equations
Symmetry
Viscous fluids
Title Symmetry-invariant conservation laws of partial differential equations
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