2007/02/27 by C. J. Cotter, C.J Cotter, D. D. Holm +3 · 46 citations
Mathematics · Physics and Astronomy · #Conservation law #Eulerian path #Flow (mathematics) #Fluid dynamics #Inverse #Inverse problem #Lagrangian #Model Reduction and Neural Networks #Momentum (technical analysis) #Numerical methods for differential equations #Quantum chaos and dynamical systems #Symmetry (geometry) #math.DS #nlin.SI
paper · pdf · doi:10.1098/rspa.2007.1892
published in Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences 463(2086), 2671-2687 (Royal Society)
arxiv created 2007/02/27 · openalex publication_date 2007/07/31 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We construct multisymplectic formulations of fluid dynamics using the inverse of the Lagrangian path map. This inverse map, the ‘back-to-labels’ map, gives the initial Lagrangian label of the fluid particle that currently occupies each Eulerian position. Explicitly enforcing the condition that the fluid particles carry their labels with the flow in Hamilton's principle leads to our multisymplectic formulation. We use the multisymplectic one-form to obtain conservation laws for energy, momentum and an infinite set of conservation laws arising from the particle relabelling symmetry and leading to Kelvin's circulation theorem. We discuss how multisymplectic numerical integrators naturally arise in this approach.