Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Revisiting Hyperbolicity of Relativistic Fluids   Motivated by the desire for highly accurate numerical computations of compact
binary spacetimes in the era of gravitational wave astronomy, we reexamine
hyperbolicity and well-posedness of the initial value problem for popular
models of general relativistic fluids. Our analysis relies heavily on the
dual-frame formalism, which allows us to work in the Lagrangian frame, where
computation is relatively easy, before transforming to the desired Eulerian
form. This general strategy allows for the construction of compact expressions
for the characteristic variables in a highly economical manner. General
relativistic hydrodynamics (GRHD), ideal magnetohydrodynamics (GRMHD) and
resistive magnetohydrodynamics (RGRMHD) are considered in turn. In the first
case we obtain a simplified form of earlier expressions. In the second we show
that the flux-balance law formulation used in typical numerical applications is
only weakly hyperbolic and thus does not have a well-posed initial value
problem. Newtonian ideal MHD is found to suffer from the same problem when
written in flux-balance law form. An alternative formulation, closely related
to that of Anile and Pennisi, is instead shown to be strongly hyperbolic. In
the final case we find that the standard forms of RGRMHD, relying upon a
particular choice of `generalized Ohm's law', are only weakly hyperbolic. The
latter problem may be rectified by adjusting the choice of Ohm's law, but we do
not do so here. Along the way weak hyperbolicity of the field equations for
dust and charged dust is also observed. More sophisticated systems, such as
multi-fluid and elastic models are also expected to be amenable to our
treatment.

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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
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The categories of this paper are: physics
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The categories of this paper are: chao-dyn
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The categories of this paper are: supr-con
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg