Rough solutions of the Einstein-vacuum equations

• Autores: Sergiu Klainerman, Igor Rodnianski
• Localización: Annals of mathematics, ISSN 0003-486X, Vol. 161, Nº 3, 2005, págs. 1143-1193
• Idioma: inglés
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• Resumen

  • 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.