Lojasiewicz-Simon gradient inequalities for coupled Yang-Mills energy functionals

In this sequel to arXiv:1510.03817, we apply our abstract Lojasiewicz-Simon gradient inequality to prove Lojasiewicz-Simon gradient inequalities for coupled Yang-Mills energy functionals using Sobolev spaces which impose minimal regularity requirements on pairs of connections and sections. The Lojasiewicz-Simon gradient inequalities for coupled Yang-Mills energy functionals generalize that of the pure Yang-Mills energy functional due to the first author (Theorem 22.8 in arXiv:1409.1525) for base manifolds of arbitrary dimension and due to Rade (1992) for dimensions two and three.