Abstract

I shall start by presenting the Einstein-Yang-Mils system and by writing it in the Lorenz gaugeand in wave coordinates as a coupled system of non-linear hyperbolic partial differential equationsand l will then show how one constructs the initial data for a Cauchy hyperbolic formulation of theproblem, Thereafter, l will present the idea behind the proof of the non-inear stability of theMinkowski space-time, solution to the Einstein-Yang-Mills eguations, in the Lorenz gauge and inwave coordinates, in all space dimensions greater or equal to three, based on a continuityargument for a higher order weighted energy norm. in the critical case of three space-dimensions.we use a null frame decomposition, that was first used by Lindblad and Rodnianski for the Einsteinvacuum equations. We then deal with new difficulties that do not exist for Einstein vacuum nor forEinstein-Maxwell fields. In particular, we treat new terms that have a different structure in the non-linearities, and we derive a more refined formula to estimate the commutator temm. This provides anew independent proof of the result by Mondal and Yau, that l posted on arXiv in a series of threepapers that build up on each other, which cover all space dimensions greater or equal to three.