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

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.

More explanatory material and title, as will appear in the published article in Classical and Quantum Gravity

References in corpus (3)

• Head-on collisions of boson stars
• An explicit harmonic code for black-hole evolution using excision
• Constraint-preserving Sommerfeld conditions for the harmonic Einstein equations

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• From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity
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• Outer boundary conditions for Einstein's field equations in harmonic coordinates
• Constraint-preserving boundary treatment for a harmonic formulation of the Einstein equations
• Geometrization of metric boundary data for Einstein's equations
• Report on GRG18, Session A3, Mathematical Studies of the Field Equations