Rough solutions of the Einstein-vacuum equations

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.

Authors

Sergiu Klainerman

Department of Mathematics
Princeton University
Princeton, NJ 08544
United States

Igor Rodnianski

Department of Mathematics
Princeton University
Princeton, NJ 08544
United States