2013/10/31 by François Gay–Balmaz, François Gay-Balmaz, Darryl D. Holm
Engineering · Mathematics · Physics and Astronomy · #Casimir effect #Classical mechanics #Cosmology and Gravitation Theories #Energy (signal processing) #Fluid Dynamics and Turbulent Flows #Ideal (ethics) #Lie algebra #Magnetohydrodynamics #Mathematical physics #Mathematics #Physics #Plasma #Pure mathematics #Quantum Electrodynamics and Casimir Effect #Quantum mechanics #math-ph #math.MP #physics.flu-dyn #physics.plasm-ph
paper · pdf · doi:10.1088/0951-7715/27/8/1747
published as Nonlinearity 27, 1747-1777 (2014) · As published
openalex publication_date 2014/07/21 · arxiv created 2018/10/20 · arxiv updated 2018/10/23 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/05
Modifications of the equations of ideal fluid dynamics with advected quantities are introduced that allow selective decay of either the energy h or the Casimir quantities C in the Lie–Poisson (LP) formulation. The dissipated quantity (energy or Casimir, respectively) is shown to decrease in time until the modified system reaches an equilibrium state consistent with ideal energy-Casimir equilibria, namely δ ( h + C ) = 0. The result holds for LP equations in general, independently of the Lie algebra and the choice of Casimir. This selective decay process is illustrated with a number of examples in 2D and 3D magnetohydrodynamics.