Rough solutions of the Einstein-vacuum equations

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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.

Original languageEnglish (US)
Pages (from-to)1143-1193
Number of pages51
JournalAnnals of Mathematics
Issue number3
StatePublished - May 2005

All Science Journal Classification (ASJC) codes

  • Mathematics (miscellaneous)


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