MG11 
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Post-Newtonian expansions for perfect fluids

Post-Newtonian expansions are expansions of solutions to the Einstein fields equations coupled to matter in a parameter v/c (near v/c=0) where v is a characteristic velocity scale of the gravitating matter and c is the speed of light. This problem has been studied for many years by many people and there is an extremely large number of results available in the literature. However, the overwhelming majority of results are based on formal expansions in the parameter v/c which lack rigorous error estimates needed to ensure the validity of the expansions as an approximation. In this talk, I will describe recent rigorous results on post-Newtonian expansions for perfect fluids. I will discuss how energy estimates for symmetric hyperbolic PDEs can be used to analyze general relativistic solutions in the singular limit v/c -> 0 and also to derive error estimates for certain expansions in v/c near v/c=0. Finally, I will discuss open problems and future research directions.