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arXiv · 0903.4294

The Geometric Structure of Complex Fluids

François Gay-Balmaz·Tudor S. Ratiu
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Abstract

This paper develops the theory of affine Euler-Poincaré and affine Lie-Poisson reductions and applies these processes to various examples of complex fluids, including Yang-Mills and Hall magnetohydrodynamics for fluids and superfluids, spin glasses, microfluids, and liquid crystals. As a consequence of the Lagrangian approach, the variational formulation of the equations is determined. On the Hamiltonian side, 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.

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François Gay-Balmaz, Tudor S. Ratiu. 2009-03-25. The Geometric Structure of Complex Fluids. https://arxiv.org/abs/0903.4294

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