Moving Frames and Noether’s Conservation Laws – the General Case

Mansfield, Elizabeth L., Goncalves, T.M.N. (2016) Moving Frames and Noether’s Conservation Laws – the General Case. Forum of Mathematics, Sigma, 4 . ISSN 2050-5094. E-ISSN 2050-5094. (doi:10.1017/fms.2016.24)

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http://dx.doi.org/10.1017/fms.2016.24

Abstract

In recent works [1, 2], the authors considered various Lagrangians, which are invariant under a Lie group action, in the case where the independent variables are themselves invariant. Using a moving frame for the Lie group action, they showed how to obtain the invariantized Euler-Lagrange equations and the space of conservation laws in terms of vectors of invariants and the adjoint representation of a moving frame. In this paper, we show how these calculations extend to the general case where the independent variables may participate in the action. We take for our main expository example the standard linear action of SL(2) on the two independent variables. This choice is motivated by applications to variational fluid problems which conserve potential vorticity. We also give the results for Lagrangians invariant under the standard linear action of SL(3) on the three independent variables.

Item Type: Article
DOI/Identification number: 10.1017/fms.2016.24
Projects: [UNSPECIFIED] Group actions in function approximation spaces
Subjects: Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, Calculus
Q Science > QA Mathematics (inc Computing science) > QA377 Partial differential equations
Q Science > QA Mathematics (inc Computing science) > QA387 Basic Lie theory
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Depositing User: Elizabeth L Mansfield
Date Deposited: 10 Jun 2015 09:57 UTC
Last Modified: 29 May 2019 14:42 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/48996 (The current URI for this page, for reference purposes)
Mansfield, Elizabeth L.: https://orcid.org/0000-0002-6778-2241
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