9400258 Klainerman A central theme of this mathematical research in the theory of nonlinear partial differential equations of evolution is that of regularity or break-down of solutions to the important examples which model the physical world. The work concerns not only what is meant by a solution but also understanding from a physical point of view the very limits of validity of the corresponding physical theories. This research is directed at specific goals in this regard - the development of relevant new techniques such as global stability of the Minkowski space-time and the analysis of the Einstein and other classical field theories. A primary goal is to study and lower, where possible, the regularity requirements on the initial data sets which assure that the initial value problem is well posed. Examples from simpler field theories suggest that the question of finding the optimal norm assuring well-posedness is intimately connected to the issue of break-down and regularity of solutions. A related direction this work will pursue concerns the question of nonlinear stability of the Minkowski metric relative to perturbations in the limited regularity class of the Einstein vacuum equations. The primary area of this project's research, nonlinearpartial differential equations, is central to the mostfundamental work currently under investigation within mathematical analysis. Solutions to nonlinear equations have been shown to posses considerable regularity and the equations themselves exhibit far more structure than was once thought possible. This project continues some of the most promising avenues of investigation in the field.
