Late-time tails of a Yang–Mills field on Minkowski and Schwarzschild backgrounds

We study the late-time behaviour of spherically symmetric solutions of the Yang–Mills equations on Minkowski and Schwarzschild backgrounds. Using nonlinear perturbation theory we show in both cases that solutions having smooth compactly supported initial data possess tails which decay as t −4 at timelike infinity. Moreover, for small initial data on Minkowski background we derive the third-order formula for the amplitude of the tail and numerically confirm its accuracy.