Symmetry transformations, isovectors, and conservation laws

DOI10.1063/1.527117zbMath0592.76005OpenAlexW2089071340MaRDI QIDQ3722031

Giacomo Caviglia

Publication date: 1986

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.527117

zbMATH Keywords

conservation lawsymmetry transformationNoether's theoremisovectorsprinciplegroup properties of the Navier-Stokes equationsinvariance properties of Hamilton's variationalnatural conserved current

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Navier-Stokes equations (35Q30) Applications of manifolds of mappings to the sciences (58D30) Foundations of fluid mechanics (76A02) Axiomatics, foundations (70A05) Generalities, axiomatics, foundations of continuum mechanics of solids (74Axx)

Related Items

Conservation laws for 3-dimensional compressible Euler equations ⋮ Symmetry-invariant conservation laws of partial differential equations ⋮ Symmetry actions and brackets for adjoint-symmetries. I: Main results and applications ⋮ Noether-type conservation laws for perfect fluid motions ⋮ The inverse problem in the calculus of variations and the geometry of the tangent bundle ⋮ An application of solvable structures to classical and nonclassical similarity solutions ⋮ Symmetries and first integrals in the mechanics of infinite-dimensional systems ⋮ Composite variational principles and the determination of conservation laws ⋮ On the incompleteness of Ibragimov's conservation law theorem and its equivalence to a standard formula using symmetries and adjoint-symmetries

Cites Work

• Group analysis and constitutive laws for fluid filled elastic tubes
• Group properties and new solutions of Navier-Stokes equations
• The infinitesimal group of the Navier-Stokes equations
• Isovector fields for problems in the mechanics of solids and fluids
• Necessary and sufficient conditions for the existence of a Lagrangian in field theory. I: Variational approach to selfadjointness for tensorial field equations
• Group analysis for a linear hyperbolic equation arising from a quasilinear reducible system
• Dynamical symmetries: An approach to Jacobi fields and to constants of geodesic motion
• Dynamical symmetries, first integrals and the inverse problem of Lagrangian dynamics
• Generalizations of Noether’s Theorem in Classical Mechanics
• A further note on the Hénon–Heiles problem
• The inverse problem of the calculus of variations applied to continuum physics
• Symmetry groups and conserved quantities for the harmonic oscillator
• Geometric Approach to Invariance Groups and Solution of Partial Differential Systems
• Conservation laws for shallow water waves on a sloping beach