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.
@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},
publisher = {Institut des hautes \'etudes scientifiques & Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
year = {2019-2020},
doi = {10.5802/slsedp.136},
zbl = {07436147},
language = {en},
url = {https://slsedp.centre-mersenne.org/articles/10.5802/slsedp.136/}
}
TY - JOUR AU - Olivier Graf TI - Problème de Cauchy spatial-caractéristique avec courbure $L^2$ en relativité générale JO - Séminaire Laurent Schwartz — EDP et applications N1 - talk:3 PY - 2019-2020 PB - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique UR - https://slsedp.centre-mersenne.org/articles/10.5802/slsedp.136/ UR - https://zbmath.org/?q=an%3A07436147 UR - https://doi.org/10.5802/slsedp.136 DO - 10.5802/slsedp.136 LA - en ID - SLSEDP_2019-2020____A2_0 ER -
%0 Journal Article %A Olivier Graf %T Problème de Cauchy spatial-caractéristique avec courbure $L^2$ en relativité générale %J Séminaire Laurent Schwartz — EDP et applications %Z talk:3 %D 2019-2020 %I Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique %U https://doi.org/10.5802/slsedp.136 %R 10.5802/slsedp.136 %G en %F SLSEDP_2019-2020____A2_0
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. https://slsedp.centre-mersenne.org/articles/10.5802/slsedp.136/
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