On the characteristic initial value problem for nonlinear symmetric hyperbolic systems, including Einstein equations (1406.3009v2)

Abstract: We consider a characteristic initial value problem for a class of symmetric hyperbolic systems with initial data given on two smooth null intersecting characteristic surfaces. We prove existence of solutions on a future neighborhood of the initial surfaces. The general result is applied to general semilinear wave equations, as well as the Einstein equations with or without sources, and conformal variations thereof.