Communications in Mathematical Physics

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

The Newtonian Limit for Perfect Fluids

  • Todd A. OliynykEmail author


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.


Sobolev Inequality Perfect Fluid Weighted Sobolev Space Newtonian Limit Symmetric Hyperbolic System 
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© Springer-Verlag 2007

Authors and Affiliations

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

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