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José M. M. Senovilla Carlos F. Sopuerta Peter Szekeres 《General Relativity and Gravitation》1998,30(3):389-411
In this paper we provide fully covariant proofs of some theorems on shear-free perfect fluids. In particular, we explicitly show that any shear-free perfect fluid with the acceleration proportional to the vorticity vector (including the simpler case of vanishing acceleration) must be either non-expanding or non-rotating. We also show that these results are not necessarily true in the Newtonian case, and present an explicit comparison of shear-free dust in Newtonian and relativistic theories in order to see where and why the differences appear. 相似文献
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In this paper a proof of existence and non-existence of theconically self-similar free-vortex solutions to the Navier-Stokesequations, originally found by Yih et al. (1982, Phys. Fluids.25, 2147-2158), is presented. This proof clearly establishesthat these solutions do not have any kind of singularity atthe symmetry axis. This analysis gives considerably improvedexistence and non-existence bounds and it is shown that thesebounds are close to optimal in the low-swirling limit. Thisapproach links the questions of existence and non-existencefor the swirling case and for the non-swirling case. The proof,which is an extension of techniques developed by Serrin (1972,Phil. Trans. R. Soc. Lond. 271, 325-360), is based on Schauder'sFixed Point Theorem and is, therefore, non-constructive. Therefore,the paper ends with a brief discussion of the question of howto compute the conically self-similar free-vortex solutionsto the Navier-Stokes equations. 相似文献
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We consider brane world scenarios including the leading correction to the Einstein-Hilbert action suggested by superstring theory, the Gauss-Bonnet term. We obtain and study the complete set of equations governing the cosmological dynamics. We find they have the same form as those in Randall-Sundrum scenarios but with time-varying four-dimensional gravitational and cosmological constants. By studying the bulk geometry we show that this variation is produced by bulk curvature terms parametrized by the mass of a black hole. Finally, we show there is a coupling between these curvature terms and matter that can be relevant for early universe cosmology. 相似文献
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