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We study the late-time behavior of spherically symmetric solutions of theYang-Mills equations on Minkowski and Schwarzschild backgrounds. Usingnonlinear perturbation theory we show in both cases that solutions havingsmooth compactly supported initial data posses tails which decay as $t^{-4}$ attimelike infinity. Moreover, for small initial data on Minkowski background wederive the third-order formula for the amplitude of the tail and confirmnumerically its accuracy.

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