Rough solutions of the Einstein vacuum equations

We announce a new result, contained in [10-12], concerning rough solutions to Einstein vacuum equations expressed relative to wave coordinates. Our methods blend paradifferential techniques with a geometric approach to Strichartz type inequlities, which takes advantage of the specific structure of the Einstein equations. This results in a gain of half a derivative relative to the classical result of [3] and [5]. 2002 Academie des science/Editions scientifiques et medicales Elsevier SAS.