Analytic Methods in the Study of the Initial Value Problem

Abstract

The goal of this chapter is to introduce the reader to the global analytic methods that play a fundamental role in the remaining chapters of the book. We start with a discussion of local and global existence results for systems of nonlinear wave equations. As we have pointed out in the previous sections, the Einstein vacuum equations can be reduced to such systems of partial differential equations with the help of wavelike coordinates. Thus the general framework of systems of nonlinear wave equations provides a very convenient first introduction to some of the basic analytic tools in the study of the evolution problem in general relativity.