Rough solutions of the Einstein vacuum equations
[Solutions peu régulières des équations d'Einstein dans le vide]
Klainerman, Sergiu1 ; Rodnianski, Igor1
1 Department of Mathematics, Princeton University, Princeton, NJ 08544, USA
Comptes Rendus. Mathématique, Tome 334 (2002) no. 2, pp. 125-130.

Nous annonçons un nouveau résultat concernant des solutions peu régulières des équations d'Einstein dans le vide exprimées en coordonnées d'ondes. Nos méthodes combinent les techniques paradifférentielles avec une approche géométrique pour les inégalités de type Strichartz, qui utilise la structure spécifique des équations d'Einstein. Cela permet de gagner une demi dérivée par rapport aux résultats classiques de [3] et [5].

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].

Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(02)02214-8
Klainerman, Sergiu 1 ; Rodnianski, Igor 1

1 Department of Mathematics, Princeton University, Princeton, NJ 08544, USA 
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Klainerman, Sergiu; Rodnianski, Igor. Rough solutions of the Einstein vacuum equations. Comptes Rendus. Mathématique, Tome 334 (2002) no. 2, pp. 125-130. doi : 10.1016/S1631-073X(02)02214-8. http://archive.numdam.org/articles/10.1016/S1631-073X(02)02214-8/

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