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  The Newtonian limit for perfect fluids

Oliynyk, T. A. (2007). The Newtonian limit for perfect fluids. Communications in Mathematical Physics, 276(1), 131-188. doi:10.1007/s00220-007-0334-z.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-48A8-4 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-48A9-2
Genre: Journal Article

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CMP276_131.pdf (Publisher version), 497KB
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 Creators:
Oliynyk, Todd A.1, Author
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1Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24012              

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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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Language(s): eng - English
 Dates: 2007
 Publication Status: Published in print
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 Identifiers: eDoc: 281820
DOI: 10.1007/s00220-007-0334-z
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Title: Communications in Mathematical Physics
Source Genre: Journal
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Pages: - Volume / Issue: 276 (1) Sequence Number: - Start / End Page: 131 - 188 Identifier: -