In this section, I analyze the role the constraint equations play
in these new formulations. I will start by analyzing how the
equations were handled in the original proof of well posedness.
Then I discuss what has been said recently and what has to be
done in the future, both for theoretical considerations and for
numerical work. In particular, I discuss the role of the
constraints in the initial-boundary value problem, a problem
which has still to be fully solved, but which nevertheless is
applied in most of the numerical simulations.