The Newtonian limit for perfect fluids

Details The Newtonian limit for perfect fluids The Newtonian limit for perfect fluids

2008-10-21

arxiv.org/abs/0810.3744v2

Comm.Math.Phys.276:131-188,2007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Differs slightly from the published version

Scientific paper

10.1007/s00220-007-0334-z

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 $\ep = v_T/c$ 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 $\ep$ independent energy estimates on weighted Sobolev spaces. These estimates are the main tool used to analyze the behavior of solutions in the limit $\ep \searrow 0$.

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