Global existence of coupled Yang-Mills and scalar fields in 2 + 1 dimensional space-time

We present results on the Cauchy problem for coupled classical Yang-Mills and scalar fields in n + 1 dimensional space-time both in the temporal and in the Lorentz gauge. We prove the existence of local solutions for any n, and the existence of global solutions for n = 1, 2 in the temporal gauge and for n = 1 in the Lorentz gauge. The last result also holds for massive Yang-Mill fields.