Recent developments in nonlinear hyperbolic PDE (Q2747951)

The author discusses some recent problems in the development of methods for attacking the central questions of the formation and structure of singularities as well as of global regularity for solutions of the Cauchy problem for nonlinear systems of partial differential equations of hyperbolic type. Applications to the Einstein equations of general relativity are particularly emphasized and detailed. He considered the constraint equations and discussed ``the future development''. The compressible Euler equations are discussed as well. The first question posed in the initial value problem is the local existence and uniqueness of the solutions. The local uniqueness theorem for Einstein's equations and compressible Euler's equations takes the form as a domain of dependence theorem. Existence of global solutions is discussed as well.