Problème de Cauchy spatial-caractéristique avec courbure $L^2$ en relativité générale

Graf, Olivier

Séminaire Laurent Schwartz — EDP et applications (2019-2020), Exposé no. 3, 16 p.

The present article is a summary of the papers [10] and [11] which establish a bounded $L^2$ 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 $L^2$ curvature fluxes through the initial spacelike and initial characteristic hypersurfaces and on suitable additional low regularity assumptions.

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