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April 2012 The fast Newtonian limit for perfect fluids
Todd A. Oliynyk
Adv. Theor. Math. Phys. 16(2): 359-391 (April 2012).

Abstract

We prove the existence of a large class of dynamical solutions to the Einstein–Euler equations for which the fluid density and spatial three-velocity converge to a solution of the Poisson–Euler equations of Newtonian gravity. The results presented here generalize those of The Newtonian limit for perfect fluids to allow for a larger class of initial data. As in The Newtonian limit for perfect fluids, the proof is based on a nonlocal symmetric hyperbolic formulation of the Einstein–Euler equations, which contain a singular parameter $\epsilon = v_T /c$ with $v_T$ a characteristic speed associated to the fluid and $c$ the speed of light. Energy and dispersive estimates on weighted Sobolev spaces are the main technical tools used to analyze the solutions in the singular limit $\epsilon \searrow 0$.

Citation

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Todd A. Oliynyk. "The fast Newtonian limit for perfect fluids." Adv. Theor. Math. Phys. 16 (2) 359 - 391, April 2012.

Information

Published: April 2012
First available in Project Euclid: 23 January 2013

zbMATH: 1269.83039
MathSciNet: MR3019408

Rights: Copyright © 2012 International Press of Boston

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Vol.16 • No. 2 • April 2012
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