Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2009-08-31
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Typos corrected. Style file changed to ATMP
Scientific paper
We prove the existence of a large class of dynamical solutions to the Einstein-Euler equations for which the fluid density and spatial three-velocity converge to a solution of the Poisson-Euler equations of Newtonian gravity. The results presented here generalize those of \cite{Oli06} to allow for a larger class of initial data. As in \cite{Oli06}, the proof is based on a non-local symmetric hyperbolic formulation of the Einstein-Euler equations which contain a singular parameter $\ep=v_T/c$ with $v_T$ a characteristic speed associated to the fluid and $c$ the speed of light. Energy and dispersive estimates on weighted Sobolev spaces are the main technical tools used to analyze the solutions in the singular limit $\ep\searrow 0$.
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