Global existence of time-dependent Yang-Mills-Higgs monopoles

We study the Cauchy problem for non-abelian Yang-Mills-Higgs theory in (3+1)-dimensional Minkowski spacetime. With suitable conditions on the background fields and a suitable choice of a Sobolev space for the subtracted gauge potentials and the Higgs field, we establish local existence. We then prove global existence by showing that an appropriate norm of the solutions cannot blow up in a finite time.