For the vacuum Einstein equations it is not
*a priori*
clear that it is even possible to find a well-posed initial
boundary value problem. Thus, it is particularly interesting that
Friedrich and Nagy [107] have been able to prove the well-posedness of certain initial
boundary value problems for the vacuum Einstein equations. Since
boundary conditions come up quite naturally when the Einstein
equations are solved numerically, due to the need to use a finite
grid, the results of [107] are potentially important for numerical relativity. The
techniques developed there could also play a key role in the
study of the initial value problem for fluid bodies (cf.
Section
2.6).

Theorems on Existence and Global Dynamics for the
Einstein Equations
Alan D. Rendall
http://www.livingreviews.org/lrr-2002-6
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