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Communications in Mathematical Physics

, Volume 276, Issue 1, pp 131–188 | Cite as

The Newtonian Limit for Perfect Fluids

  • Todd A. OliynykEmail author
Article

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.

Keywords

Sobolev Inequality Perfect Fluid Weighted Sobolev Space Newtonian Limit Symmetric Hyperbolic System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Max-Planck-Institut für GravitationsphysikGolmGermany
  2. 2.School of Mathematical SciencesMonash UniversityClaytonAustralia

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