The present article is a summary of the papers [10] and [11] which establish a bounded curvature theorem for the spacelike-characteristic Cauchy problem of general relativity. More precisely, we obtain a lower bound on the time of existence of classical solutions to the spacelike-characteristic Cauchy problem for Einstein equations in vacuum, depending only on the curvature fluxes through the initial spacelike and initial characteristic hypersurfaces and on suitable additional low regularity assumptions.
Olivier Graf. Problème de Cauchy spatial-caractéristique avec courbure $L^2$ en relativité générale. Séminaire Laurent Schwartz — EDP et applications (2019-2020), Talk no. 3, 16 p.. doi: 10.5802/slsedp.136
@article{SLSEDP_2019-2020____A2_0,
author = {Olivier Graf},
title = {Probl\`eme de {Cauchy} spatial-caract\'eristique avec courbure~$L^2$ en relativit\'e g\'en\'erale},
journal = {S\'eminaire Laurent Schwartz {\textemdash} EDP et applications},
note = {talk:3},
pages = {1--16},
year = {2019-2020},
publisher = {Institut des hautes \'etudes scientifiques & Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
doi = {10.5802/slsedp.136},
zbl = {07436147},
language = {en},
url = {https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.136/}
}
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