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The Newtonian Limit for Perfect Fluids

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Abstract

We prove that there exists a class of non-stationary solutions to the Einstein-Euler equations which have a Newtonian limit. The proof of this result is based on a symmetric hyperbolic formulation of the Einstein-Euler equations which contains a singular parameter ∈ =  v T /c, where v T is a characteristic velocity scale associated with the fluid and c is the speed of light. The symmetric hyperbolic formulation allows us to derive ε independent energy estimates on weighted Sobolev spaces. These estimates are the main tool used to analyze the behavior of solutions in the limit ∈ ↘ 0.

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  1. Todd A. Oliynyk

    Present address: School of Mathematical Sciences, Monash University, Clayton, Vic, 3800, Australia

Authors and Affiliations

  1. Max-Planck-Institut für Gravitationsphysik, Am Mühlenberg 1, D-14476, Golm, Germany

    Todd A. Oliynyk

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  1. Todd A. Oliynyk
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Correspondence to Todd A. Oliynyk.

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Communicated by G.W. Gibbons

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Oliynyk, T.A. The Newtonian Limit for Perfect Fluids. Commun. Math. Phys. 276, 131–188 (2007). https://doi.org/10.1007/s00220-007-0334-z

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