Abstract
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 language | English (US) |
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Pages (from-to) | 1143-1193 |
Number of pages | 51 |
Journal | Annals of Mathematics |
Volume | 161 |
Issue number | 3 |
DOIs | |
State | Published - May 2005 |
All Science Journal Classification (ASJC) codes
- Mathematics (miscellaneous)