530 research outputs found
Nonexistence of smooth solutions for the general compressible Ericksen -- Leslie equations in three dimensions
We prove that the smooth solutions to the Cauchy problem for the compressible
general three-dimensional Ericksen--Leslie system modeling nematic liquid
crystal flow with conserved mass, linear momentum, and dissipating total
energy, generally lose classical smoothness within a finite time.Comment: 7 pages. arXiv admin note: text overlap with arXiv:1206.2850,
arXiv:1105.2180 by other author
Invariant generators for generalized distributions
The existence of invariant generators for distributions satisfying a
compatibility condition with the symmetry algebra is proved
Banach Lie-Poisson spaces and reduction
The category of Banach Lie-Poisson spaces is introduced and studied. It is
shown that the category of W*-algebras can be considered as one of its
subcategories. Examples and applications of Banach Lie-Poisson spaces to
quantization and integration of Hamiltonian systems are given. The relationship
between classical and quantum reduction is discussed.Comment: 58 pages, to apear in Comm.Math.Phy
The Geometric Structure of Complex Fluids
This paper develops the theory of affine Euler-Poincar\'e 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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