On Noether’s Theorem for the Euler–Poincaré Equation on the Diffeomorphism Group with Advected Quantities

• Published in: Foundations of computational mathematics Vol. 13; no. 4; pp. 457 - 477
• Main Authors: Cotter, C. J., Holm, D. D.
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.08.2013; Springer; Springer Nature B.V
• Subjects: Applications of Mathematics; Computational mathematics; Computer Science; Conservation laws; Density; Differential equations; Economics; Eulers equations; Evolution; Linear and Multilinear Algebras; Math Applications in Computer Science; Mathematical analysis; Mathematical models; Mathematics; Mathematics and Statistics; Matrix Theory; Numerical Analysis; Symmetry; Theorems; Theorems (Mathematics); Vector space; Vector spaces; Vectors (mathematics); United Kingdom; Conservation laws; Hamiltonian structures; Symmetries; 37K05; Variational principles

We show how Noether conservation laws can be obtained from the particle relabelling symmetries in the Euler–Poincaré theory of ideal fluids with advected quantities. All calculations can be performed without Lagrangian variables, by using the Eulerian vector fields that generate the symmetries, and...