Well-posed initial-boundary value problem for the harmonic Einstein equations using energy estimates

TL;DR

This paper demonstrates that the initial-boundary value problem for harmonic Einstein equations is strongly well-posed using standard energy estimates, providing a classical proof of well-posedness for these equations.

Contribution

It shows that strong well-posedness of the harmonic Einstein equations can be established through energy estimates, complementing previous pseudo-differential approaches.

Findings

Strong well-posedness established using energy estimates

Classical energy methods applicable to Einstein equations

Provides a more accessible proof of well-posedness

Abstract

In recent work, we used pseudo-differential theory to establish conditions that the initial-boundary value problem for second order systems of wave equations be strongly well-posed in a generalized sense. The applications included the harmonic version of the Einstein equations. Here we show that these results can also be obtained via standard energy estimates, thus establishing strong well-posedness of the harmonic Einstein problem in the classical sense.