The Fuchsian approach to global existence for hyperbolic equations

In this thesis we apply a new method to obtain global existence solutions of wave equations on Minkowski and Schwarzschild space-times with quadratic terms that satisfy the null condition and in the case of Minkowski space-time, a restricted version of the weak null condition. Introducing suitable variables, we transform these wave equations into first order symmetric hyperbolic Fuchsian equations, such that they are defined on a bounded space-time region. This allow us to apply the existence theory from [1], which by construction, yields solutions to the original system of wave equations on a neighbourhood of spatial infinity.