5 M ar 2 00 9 Affine Lie - Poisson Reduction , Yang - Mills magnetohydrodynamics , and superfluids
نویسنده
چکیده
where ρ is the mass density, S is the entropy density, and p is the pressure. It was shown in Morrison and Greene [1980] that this system, as well as its magnetohydrodynamic extension, admit a noncanonical Poisson formulation, that is, equation (1.1) can be written as ḟ = {f, h}, relative to a Hamiltonian function h. The study of the relativistic case was initiated in Bia lynicki-Birula, Hubbard, and Turski [1983], Mayer [1984], and Holm and Kupershmidt [1984a]. The present paper considers only non-relativistic fluids. It is of great (mathematical and physical) interest to obtain these Poisson brackets by a reduction procedure from a canonical Hamiltonian formulation on a cotangent bundle. In Marsden, Ratiu, and Weinstein [1984], the noncanonical Poisson bracket associated to Section de Mathématiques and Bernoulli Center, École Polytechnique Fédérale de Lausanne. CH–1015 Lausanne. Switzerland. [email protected], [email protected]
منابع مشابه
Affine Lie–Poisson reduction, Yang–Mills magnetohydrodynamics, and superfluids
This paper develops the theory of affine Lie–Poisson reduction and applies this process to Yang–Mills and Hall magnetohydrodynamics for fluids and superfluids. As a consequence of this approach, the associated Poisson brackets are obtained by reduction of a canonical cotangent bundle. A Kelvin–Noether circulation theorem is presented and is applied to these examples. PACS numbers: 02.20.Sv, 47....
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