Geodesic
Rough solutions of the Einstein-vacuum equations
Sergiu Klainerman1 ; Igor Rodnianski2
1 Department of Mathematics, Princeton University, Princeton, NJ 08544, United States
2 Department of Mathematics, Princeton University, Princeton, NJ 08544, United States
Annals of mathematics, Tome 161 (2005) no. 3, pp. 1143-1193.

Voir la notice de l'article provenant de la source Annals of Mathematics website

This is the first in a series of papers in which we initiate the study of very rough solutions to the initial value problem for the Einstein-vacuum equations expressed relative to wave coordinates. By very rough we mean solutions which cannot be constructed by the classical techniques of energy estimates and Sobolev inequalities. Following [Kl-Ro] we develop new analytic methods based on Strichartz-type inequalities which result in a gain of half a derivative relative to the classical result. Our methods blend paradifferential techniques with a geometric approach to the derivation of decay estimates. The latter allows us to take full advantage of the specific structure of the Einstein equations.
DOI : 10.4007/annals.2005.161.1143

Sergiu Klainerman 1 ; Igor Rodnianski 2

1 Department of Mathematics, Princeton University, Princeton, NJ 08544, United States
2 Department of Mathematics, Princeton University, Princeton, NJ 08544, United States 
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Sergiu Klainerman; Igor Rodnianski. Rough solutions of the Einstein-vacuum equations. Annals of mathematics, Tome 161 (2005) no. 3, pp. 1143-1193. doi : 10.4007/annals.2005.161.1143. http://geodesic.mathdoc.fr/articles/10.4007/annals.2005.161.1143/

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