Titlebook: Magnetohydrodynamics and Fluid Dynamics: Action Principles and Conservation Laws; Gary Webb Book 2018 Springer International Publishing AG

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,Euler-Poincaré Equation Approach,wed that the equations for ideal, incompressible fluid dynamics could be derived from a variational principle in which the Lagrangian consists of the fluid kinetic energy, subject to an infinite Lie group (pseudo-Lie group) constraint, associated with the Lagrangian map (the constraint is that the L

Concerto

Hamiltonian Approach,range multipliers to enforce the constraints of mass conservation; the entropy advection equation; Faraday’s equation and the so-called Lin constraint describing in part, the vorticity of the flow (i.e. Kelvin’s theorem). This leads to Hamilton’s canonical equations in terms of Clebsch potentials. T

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Morose

MEN

MHD Stability,bria was investigated in the seminal paper by Bernstein et al. (.) who derived sufficient conditions for magneto-static equilibria, based on the so-called energy principle. A sufficient, but not necessary condition for magnetostatic equilibria is that the potential energy functional .(., .) satisfie

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Conscientious

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Introduction,for systems of differential equations governed by an action principle. Noether’s theorem applies to systems of Euler-Lagrange equations that are in Kovalevskaya form (e.g Olver (1993)). For other Euler-Lagrange systems, each nontrivial variational symmetry leads to a conservation law, but there is no guarantee that it is non-trivial.