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arXiv · 1007.4302

One-Dimensional Approximation of Viscous Flows

Umpei Miyamoto
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Abstract

Attention has been paid to the similarity and duality between the Gregory-Laflamme instability of black strings and the Rayleigh-Plateau instability of extended fluids. In this paper, we derive a set of simple (1+1)-dimensional equations from the Navier-Stokes equations describing thin flows of (non-relativistic and incompressible) viscous fluids. This formulation, a generalization of the theory of drop formation by Eggers and his collaborators, would make it possible to examine the final fate of Rayleigh-Plateau instability, its dimensional dependence, and possible self-similar behaviors before and after the drop formation, in the context of fluid/gravity correspondence.

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Umpei Miyamoto. 2010-08-07. One-Dimensional Approximation of Viscous Flows. https://doi.org/10.1007/jhep10(2010)011

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